Magnetic Effects of Electric Current

Correct Option: (C) The same at all points — The magnetic field lines inside a long straight solenoid carrying current are parallel straight lines along its axis, indicating that the magnetic field is uniform and of the same strength at all points inside.

Correct Option: (B) A moving charge — A stationary charge produces only an electrostatic field. A moving charge (electric current) produces both an electric field and a magnetic field (Oersted's discovery).

Correct Option: (B) From South to North — Outside a bar magnet, field lines emerge from the North pole and enter the South pole. To complete closed continuous loops, inside the magnet they direct from South to North.

Correct Option: (D) Zero — Magnetic Lorentz force on a charge $q$ moving with velocity $v$ in magnetic field $B$ is $F = qvB\sin heta$. For a stationary charge ($v = 0$), the magnetic force is zero.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — If two magnetic field lines intersected at a point, a compass needle placed at that point would point in two different directions at the same time, which is physically impossible.

Magnetic Field: The region surrounding a magnet or current-carrying conductor in which its magnetic force or influence can be experienced by a magnetic substance or compass.

SI Unit: The SI unit of magnetic field is Tesla (T) (or $\text{Weber}/\text{m}^2$).

The magnetic field lines around a straight current-carrying conductor are concentric circles centered on the conductor, lying in a plane perpendicular to the wire.

Two properties of magnetic field lines:

1. They emerge from the North pole and merge at the South pole outside the magnet, continuing from South to North inside to form closed continuous loops.
2. No two field lines ever intersect each other at any point.

Identification of poles: Since magnetic field lines always emerge from North poles and enter South poles:

• Lines emerging from a pole $\implies$ North pole (N).
• Lines entering into a pole $\implies$ South pole (S).

Inference: Magnetic field lines are continuous directed curves originating from North and terminating at South outside a magnet.

Two magnetic field lines can never intersect each other because the tangent at any point on a field line gives the direction of the magnetic field at that point. If they intersect, there would be two tangents and hence two directions of magnetic field at the same point, which means a compass needle would have to point in two directions simultaneously — an impossibility.

Pattern for circular loop: Field lines are concentric circles near the wire segments. As we move towards the centre of the loop, the circles become larger and larger; at the centre, the field lines appear as parallel straight lines perpendicular to the plane of the loop.

Difference from electric field lines: Magnetic field lines form continuous closed loops (they do not start or end on magnetic monopoles), whereas electrostatic field lines are discontinuous open curves (originating on positive charges and terminating on negative charges).

(i) Inside a bar magnet, field lines travel from South pole to North pole.

(ii) Two properties: (1) They form closed continuous curves, (2) Crowding of lines indicates higher magnetic field strength.

(iii) The field is strongest near the wire. The concentric circles are closely spaced near the wire and become progressively farther apart as distance increases.

(iv) If two lines intersected, a magnetic compass placed at the intersection would have to point in two different directions at the same time, which is physically impossible.

Correct Option: (C) Right-hand thumb rule — Maxwell's Right-Hand Thumb Rule gives the direction of magnetic field lines around a straight current-carrying wire (thumb points in current direction, curled fingers give field direction).

Correct Option: (C) The current and the perpendicular distance of the point from the conductor — Magnetic field $B \propto I$ and $B \propto \frac{1}{r}$. Therefore, strength depends directly on current and inversely on distance from the wire.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Oersted proved that electric current in a wire produces a magnetic field because electric charges in motion always generate a magnetic field around them.

Right-Hand Thumb Rule (Maxwell's Corkscrew Rule):

Imagine holding a straight current-carrying conductor in your right hand such that your thumb points in the direction of the electric current. Then your curled fingers encircling the conductor point in the direction of the magnetic field lines.

Application: If current flows vertically upward, magnetic field lines are anti-clockwise when viewed from above.

Activity (Oersted's Experiment):

1. Connect a thick straight copper wire $AB$ in series with a battery, a plug key, and a rheostat.
2. Place a small magnetic compass needle directly below and parallel to the wire.
3. Close the key so that current flows through the wire from South to North.
4. Observation: The North pole of the compass needle immediately deflects towards the West (SNOW rule).
5. Reversal: When current direction is reversed (North to South), the compass needle deflects towards the East.
6. Conclusion: An electric current flowing in a conductor produces a magnetic field around it.

Two factors affecting magnetic field strength ($B$):

1. Magnitude of electric current ($I$): $B \propto I$. Increasing the current increases the strength of the magnetic field proportionally (deflection of compass needle increases).
2. Perpendicular distance from conductor ($r$): $B \propto \frac{1}{r}$. Increasing distance from the wire decreases the field strength (concentric circles become more widely spaced).

Correct Option: (B) Straight lines parallel to the axis — At the center of a circular current-carrying coil, the magnetic field lines are uniform and perpendicular to the plane of the coil (parallel straight lines).

Correct Option: (B) Every small element of the loop contributes a field in the same direction at the centre, so all fields add up — By the right-hand rule, every arc segment of the circular loop directs its magnetic field in the identical perpendicular direction at the center, leading to constructive superposition.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — All current elements of the circular loop contribute magnetic field vectors at the center directed along the central axis perpendicular to the loop's plane.

Pattern of field lines: Near the circular wire, field lines are concentric circles. As we move away from the wire towards the centre, the concentric circles become larger arcs. At the centre, the field lines become straight and parallel, running perpendicular to the plane of the loop.

Difference from a straight wire: Around a straight wire, the field lines are concentric circles throughout space, while at the centre of a circular loop, the field is uniform, straight, and concentrated along the coil's central axis.

The magnetic field at the centre of a circular coil of radius $r$ with $n$ turns carrying current $I$ is $B \propto \frac{nI}{r}$.

To increase the magnetic field strength:

1. Increase the number of turns ($n$): Each turn adds its magnetic field constructively ($B$ increases $n$-fold).
2. Increase the current ($I$): Increasing current through the coil proportionally increases $B$.
3. Decrease the radius ($r$): A smaller loop radius concentrates the field at the centre.

Correct Option: (C) Is uniform — Inside a long solenoid carrying steady direct current, field lines are parallel, equidistant straight lines, which means the magnetic field is uniform in strength and direction.

Correct Option: (D) Soft iron — Soft iron has high magnetic permeability and low retentivity: it gets strongly magnetised when current flows and loses almost all magnetism as soon as current is switched off.

Correct Option: (B) Clock face rule — The clock face rule states: looking at a face of a coil, if current flows in a clockwise direction, that face behaves as a South pole; if anticlockwise, it behaves as a North pole.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — A current-carrying solenoid produces external magnetic field lines identical to those of a bar magnet with distinct North and South magnetic poles at its two ends.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Magnetic field inside an ideal solenoid is $B = \mu_0 n I$ (where $n = N/L$ is turns per unit length), which depends only on $n$ and current $I$, being uniform throughout.

Solenoid: A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder.

Use of magnetic field inside: The strong, uniform magnetic field inside a solenoid is used to magnetise a piece of magnetic material like soft iron to produce an electromagnet.

Two properties of magnetic field lines:

1. Inside the solenoid, the field lines are parallel straight lines, showing that the magnetic field is uniform.
2. Outside, the field lines emerge from the North pole and enter the South pole, behaving exactly like a bar magnet.

Similarities between solenoid and bar magnet:

1. Both produce identical magnetic field line patterns outside (emerging from N-pole and entering S-pole).
2. Both freely align along the geographical North-South direction when suspended freely.
3. Both exhibit attraction and repulsion properties with other magnets.

Difference: The magnetic field of an electromagnet/solenoid is temporary and can be switched on/off and adjusted by varying current, whereas a bar magnet has a permanent fixed magnetic field.

(a) Comparison of field at P and Q: The magnetic field at point $P$ (middle/interior) is uniform and stronger than at point $Q$ (end). At the ends of a solenoid, the magnetic field strength is approximately half of that at the centre ($B_{\text{end}} \approx \frac{1}{2} B_{\text{centre}}$).

(b) To change field strength: Change the current flowing through the coil (using a rheostat) or insert a soft iron core inside the coil.

Electromagnet: A temporary magnet consisting of a core of magnetic material (soft iron) surrounded by a current-carrying coil of wire.

How it is made: Wound insulated copper wire around a soft iron rod and pass direct electric current through the coil.

Two differences from a permanent bar magnet:

1. An electromagnet is temporary (loses magnetism when current stops), whereas a bar magnet is permanent.
2. The magnetic strength and polarity of an electromagnet can be easily varied or reversed, whereas a bar magnet has fixed strength and polarity.

Two uses: Electric bells, electric cranes (lifting heavy iron scrap), MRI scanners, loudspeakers.

A magnetic field exerts a deflecting force on a moving charged particle perpendicular to both its velocity and the magnetic field ($F = qvB\sin\theta$). Consequently, the charged particle follows a curved or circular path without changing its speed or kinetic energy.

No, a freely suspended current-carrying solenoid cannot stay in any arbitrary direction. It always comes to rest pointing in the North-South direction because it behaves as a magnetic dipole with North and South poles, aligning itself with Earth's magnetic field.

Correct Option: (C) Force on a current-carrying conductor in a magnetic field — Fleming's Left-Hand Rule gives the direction of magnetic force (thrust) experienced by a current-carrying conductor placed in a magnetic field (applied in electric motors).

Correct Option: (B) Forefinger — In Fleming's Left-Hand Rule: Thumb = Force/Motion, Forefinger = Magnetic Field, Middle finger = Electric Current.

Correct Option: (D) 90° — The force on a current-carrying conductor is $F = BIL\sin\theta$. Since $\sin 90° = 1$ (maximum), the force is maximum when the conductor is perpendicular ($90°$) to the magnetic field.

Two devices based on the force on a current-carrying conductor in a magnetic field are: (1) Electric Motor, and (2) Moving-Coil Loudspeaker (or Galvanometer).

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — The magnetic force is given by $\vec{F} = I(\vec{L} \times \vec{B})$. Reversing the direction of current reverses the vector $\vec{L}$, thus reversing the direction of $\vec{F}$ (verified by Fleming's left-hand rule).

Fleming's Left-Hand Rule: Stretch the thumb, forefinger, and middle finger of your left hand mutually perpendicular to each other. If the forefinger points in the direction of the magnetic field and the middle finger points in the direction of the current, then the thumb points in the direction of the force (motion/thrust) acting on the conductor.

Device applied in: Electric Motor.

Activity (Kicking Wire Experiment / Rod Displacement):

1. Suspend a small aluminium rod $AB$ horizontally using two connecting wires from a stand.
2. Place a strong horseshoe magnet such that the rod lies between its two poles with magnetic field directed vertically upwards (North pole below, South pole above).
3. Connect the rod in series with a battery, key, and rheostat.
4. Pass current through the rod from $B$ to $A$.
5. Observation: The rod is observed to be displaced towards the left.
6. Reversal: On reversing current direction (from $A$ to $B$), the rod is displaced towards the right.
7. Conclusion: A current-carrying conductor in a magnetic field experiences a mechanical force whose direction depends on the directions of current and magnetic field (governed by Fleming's left-hand rule).

Effect on copper wire:

When current passes through the wire placed in the magnetic field between the poles of a horseshoe magnet, the wire experiences a mechanical force and gets deflected sideways.

Rule used: Fleming's Left-Hand Rule determines the direction of deflection.

(i) Fleming's Left-Hand Rule: Thumb = Force, Forefinger = Magnetic Field, Middle Finger = Current.

(ii) Force is maximum when conductor is perpendicular ($90°$) to the magnetic field.

(iii) If the direction of current is reversed, the direction of force on the conductor is reversed.

(iv) No force acts on the conductor when it is placed parallel ($0°$ or $180°$) to the magnetic field ($\sin 0° = 0$).

Correct Option: (B) Electrical energy into mechanical energy — An electric motor is a rotating device that converts input electrical energy into mechanical rotational kinetic energy.

Correct Option: (B) Reverses the direction of current in the coil every half rotation — The split ring commutator swaps contact with carbon brushes every half rotation, ensuring the torque acts continuously in the same direction.

Correct Option: (C) An electromagnet, large number of turns, and a soft iron core — Commercial motors enhance torque by replacing permanent magnets with powerful electromagnets, using coils with many turns of insulated wire, and winding them on a soft iron core (armature).

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Commercial motors use electromagnets and soft iron cores to produce an exceptionally strong magnetic field, maximizing rotational power.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — The split ring commutator reverses the current through each half of the armature coil every $180°$, keeping the couple of forces acting in the same rotational direction.

Function of split ring commutator: It acts as a current reverser. It reverses the direction of electric current flowing through the armature coil every half rotation ($180°$). This ensures that the forces on the two arms of the coil continue to rotate the coil in the same single direction.

Principle of an electric motor: It works on the principle of the magnetic force on a current-carrying conductor. When a rectangular current-carrying coil is placed in a magnetic field, it experiences mutually opposite forces on its opposite arms that create a torque, causing it to rotate continuously.

Two devices: Electric fans, washing machines, water pumps, refrigerators.

Construction of DC Electric Motor:

• Armature coil ($ABCD$): A rectangular loop of insulated copper wire wound on a soft iron core.
• Strong permanent magnet: Provides a uniform magnetic field across the coil.
• Split rings ($P$ and $Q$): Commutator halves attached to coil ends and rotating with it.
• Carbon brushes ($X$ and $Y$): Stationary flexible carbon blocks maintaining sliding electrical contact with split rings.

Working: Current enters arm $AB$ from brush $X$ and leaves through arm $CD$ via brush $Y$. By Fleming's left-hand rule, arm $AB$ experiences a downward force while $CD$ experiences an upward force, rotating the coil anticlockwise. After half a rotation, split rings swap brush contacts, reversing the current direction in $AB$ and $CD$ so the rotational torque continues in the identical anticlockwise direction.

Energy Conversion: Electrical energy $ o$ Mechanical energy.

Differences between commercial and simple electric motors:

1. Commercial motors use an electromagnet instead of a permanent magnet to generate a much stronger magnetic field.
2. They use a large number of turns of copper wire in the current-carrying coil.
3. The coil is wound on a soft iron core; the soft iron core plus coils is termed an armature, which dramatically increases the power of the motor.

(i) Electric motor converts electrical energy into mechanical energy.

(ii) Fleming's Left-Hand Rule is used to find the direction of rotation/force on the arms.

(iii) The split ring commutator reverses current direction every half cycle, sustaining rotation in the same direction.

(iv) The soft iron core concentrates magnetic field lines and enhances magnetic flux, greatly increasing the torque and power output.

Correct Option: (B) A momentary deflection is observed in the galvanometer — Relative motion between the magnet and coil changes the magnetic flux linked with the coil, inducing an electric current (Faraday's electromagnetic induction).

Correct Option: (C) No deflection is observed — Electromagnetic induction requires a change in magnetic flux linked with the coil over time ($e = -\frac{d\Phi}{dt}$). When the magnet is stationary, magnetic flux is constant, so induced current is zero.

Correct Option: (C) Pushed into the coil rapidly — Faraday's law states that induced EMF is directly proportional to the rate of change of magnetic flux ($e \propto \frac{\Delta \Phi}{\Delta t}$). Faster movement yields higher rate of change and larger deflection.

Correct Option: (B) Induced current in a conductor moving in a magnetic field — Fleming's Right-Hand Rule gives the direction of induced electric current in a conductor moving through a magnetic field (used in electric generators).

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Electromagnetic induction is the process by which a changing magnetic field in a region induces an electric current in another closed circuit.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — A galvanometer has its zero point in the center of its scale; it can detect even micro-amperes of current and shows the direction of current flow by deflecting to the left or right.

Electromagnetic Induction: The phenomenon of generating an induced electric current in a closed circuit/coil whenever the magnetic flux (magnetic field lines) linked with the coil changes over time.

Meaning of terms:

• 'Induced EMF / Potential Difference': The voltage produced across the ends of a conductor due to relative motion between the conductor and a magnetic field.
• 'Induced Current': The electric current that circulates through a closed circuit as a result of the induced EMF.

Observations:

1. Magnet pushed into the coil: The galvanometer needle shows a momentary deflection in one direction (e.g., to the right), indicating momentary induced current.
2. Magnet held stationary inside: The galvanometer deflection returns to zero (no change in magnetic flux $\implies$ no induced current).
3. Magnet pulled out of the coil: The galvanometer needle shows a momentary deflection in the opposite direction (to the left).

Rule: Fleming's Right-Hand Rule:

Stretch the thumb, forefinger, and middle finger of your right hand mutually perpendicular to each other. If the forefinger points in the direction of the magnetic field and the thumb points in the direction of motion of the conductor, then the middle finger points in the direction of the induced electric current.

Mutual Induction Activity:

1. When key is closed in primary coil P: Current in coil P rises from zero to maximum, causing magnetic flux around it to expand. This changing flux cuts secondary coil S, producing a momentary deflection in the galvanometer.
2. When steady current flows in P: Magnetic field is constant (rate of change of flux is zero), so galvanometer needle rests at zero.
3. When key is opened in P: Current drops to zero, causing the magnetic flux to collapse. The galvanometer needle gives a momentary deflection in the opposite direction.

Fleming's Right-Hand Rule: Stretch the thumb, forefinger, and middle finger of the right hand mutually perpendicular to each other. Forefinger points in magnetic field direction, thumb points in motion of conductor direction, and middle finger indicates the direction of induced current.

Device applied in: Electric Generator (Dynamo).

(i) Electromagnetic induction was discovered by Michael Faraday in 1831.

(ii) Fleming's Right-Hand Rule gives the direction of induced current.

(iii) When the magnet is stationary inside the coil, the deflection is zero because there is no relative motion or rate of change of magnetic flux.

(iv) Increasing the speed of the magnet increases the rate of change of magnetic flux, producing a larger induced EMF and higher galvanometer deflection.

Correct Option: (C) Generator — An electric generator converts mechanical energy into electrical energy based on electromagnetic induction.

Correct Option: (B) Mechanical energy into electrical energy — Generators take mechanical rotational work from turbines or engines and convert it into alternating or direct electrical current.

Correct Option: (B) Maintain continuous contact with the same side of the coil, allowing current direction to alternate — Full circular slip rings keep permanent contact with their respective brushes, preserving the naturally alternating EMF produced by the rotating armature.

Correct Option: (B) 50 Hz — In India, household AC supply alternates at a frequency of 50 Hz (reversing its direction every $\frac{1}{100}$ second, completing 50 full cycles per second).

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Slip rings maintain continuous contact with their specific coil terminals, ensuring the external circuit receives an alternating current that reverses polarity every half cycle.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — In India, AC has a frequency of 50 Hz. Since current changes direction twice in each full cycle, it reverses direction $50 \times 2 = 100$ times each second (every $1/100$ s).

Difference between Direct Current (DC) and Alternating Current (AC):

Working Principle of AC Generator: It works on the principle of Electromagnetic Induction. When a closed armature coil is rotated in a magnetic field, the magnetic flux linked with the coil changes continuously, inducing an alternating current in the coil.

Rule used: Fleming's Right-Hand Rule determines the direction of the induced current.

Two advantages of AC over DC:

1. Long-distance transmission with minimum loss: AC voltage can be stepped up to very high levels using step-up transformers, reducing current ($I$) and drastically cutting $I^2R$ transmission heat losses over hundreds of kilometres.
2. Ease of voltage conversion: AC voltages can be easily stepped up or stepped down to any desired level using transformers.

Two devices using AC: Refrigerators, ceiling fans, air conditioners, washing machines.

Construction of an AC Generator:

• Armature coil ($ABCD$): Rectangular coil of many turns of insulated copper wire wound on a soft iron core.
• Permanent magnet: Strong curved magnetic poles providing a uniform magnetic field.
• Slip rings ($R_1, R_2$): Two hollow brass rings connected to coil ends, rotating with the shaft.
• Carbon brushes ($B_1, B_2$): Fixed carbon blocks sliding against slip rings to tap output current.

Working: When the coil is rotated clockwise, arm $AB$ moves upwards and $CD$ moves downwards. By Fleming's right-hand rule, induced current flows along $A \to B \to C \to D$. After half a rotation, $CD$ moves up and $AB$ moves down, reversing the current direction to $D \to C \to B \to A$. Thus, the current alternates polarity every half cycle, producing Alternating Current (AC).

Differences between Electric Motor and Electric Generator:

(i) An AC generator works on the principle of Electromagnetic Induction.

(ii) Frequency of domestic AC in India is $50\text{ Hz}$; it reverses direction 100 times every second.

(iii) Slip rings are used in an AC generator, while a split ring commutator is used in a DC generator/motor.

(iv) The main advantage of AC is that it can be transmitted over long distances at high voltages with minimal loss of electrical energy.

Correct Option: (D) 220 V — In India, the electric potential difference between the live wire (at 220 V) and neutral wire (at 0 V) in domestic electricity supply is 220 V.

Correct Option: (C) Red (or brown) — Standard insulation colour code: Live wire = Red (new code: Brown), Neutral wire = Black (new code: Light Blue), Earth wire = Green (new code: Green/Yellow).

Correct Option: (C) Electric fuse — An electric fuse is a sacrificial safety device containing a low-melting wire that melts and opens the circuit during overcurrent or short circuits, protecting cables and appliances from fire.

Correct Option: (C) To prevent severe electric shock by providing a low-resistance path to earth for any leakage current — If live wire insulation wears off and contacts metallic casing, the earth wire safely routes high fault current to ground, blowing the fuse immediately.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Domestic appliances are wired in parallel so each gets full 220 V supply and can be turned on/off independently without affecting other appliances.

Correct Option: (A) Both A and R are true, and R is the correct explanation of A. — Connecting the fuse in the live wire guarantees that whenever an overcurrent occurs, the fuse blows and completely disconnects the dangerous high-voltage line from the appliance.

Three types of wires in domestic circuits:

1. Live Wire (Positive): Carries high potential of 220 V. Insulation color: Red (or Brown).
2. Neutral Wire (Negative): Completes circuit at 0 V. Insulation color: Black (or Light Blue).
3. Earth Wire: Safety wire connected to a metal plate buried deep underground. Insulation color: Green (or Green/Yellow stripes).

(i) Short Circuit: Occurs when the live wire and neutral wire come into direct physical contact (due to faulty insulation or appliance damage). Resistance drops almost to zero, causing an abnormally huge current to flow, resulting in sparking and fire hazards.

(ii) Overloading: Occurs when too many high-power electrical appliances (air conditioners, heaters, irons) are switched on simultaneously on the same circuit, or when multiple appliances are plugged into a single socket. The total current drawn exceeds the safe rated capacity of the wires, leading to overheating.

Function of Earth Wire: It provides an easy, very low-resistance conducting path to the ground for any electric current that leaks onto the metallic casing of an appliance.

Why it is necessary: If the live wire insulation is frayed and touches the metal casing of an appliance (e.g., refrigerator, iron), anyone touching the appliance would receive a fatal electric shock. The earth wire channels this fault current harmlessly into the earth, immediately triggering the fuse/MCB to blow and protecting the user from severe electric shock.

Domestic Electric Circuit System in India:

• Supply lines: Electric power enters houses via overhead cables or underground wires as Live wire (220 V) and Neutral wire (0 V).
• Main fuse: Live wire passes through an electric meter board via a company fuse ($50\text{ A}$).
• Electricity meter: Records total electrical energy consumed in kWh.
• Main switch & Distribution board: Feeds separate branch circuits via individual fuses/MCBs.
• Two standard circuits:
  1. $15\text{ A}$ power circuit: For heavy appliances (geysers, ACs, heaters).
  2. $5\text{ A}$ lighting circuit: For low-power appliances (bulbs, fans, TVs).
• Parallel arrangement: All appliances are connected in parallel so that each gets the full $220\text{ V}$ and operates independently with its own separate switch.

Differences between Fuse and MCB (Miniature Circuit Breaker):

(i) Voltage and frequency in Indian domestic circuits: $220\text{ V}$ and $50\text{ Hz}$.

(ii) Live wire colour is Red (or Brown); neutral wire is Black (or Blue).

(iii) Two reasons for parallel domestic wiring: (1) Each appliance receives full $220\text{ V}$ rated voltage, and (2) If one appliance fails or is turned off, other appliances continue working uninterrupted.

(iv) The fuse wire must have a low melting point and high resistance so that it melts rapidly and interrupts excessive current before house wiring catches fire.

(a) Electromagnetic Induction: The production of an electric current in a closed circuit by changing the magnetic field or magnetic flux linked with the circuit.

(b) Activity:

1. Take two circular coils of copper wire: Coil 1 (primary, $100$ turns) connected to a battery and a plug key, and Coil 2 (secondary, $50$ turns) connected to a sensitive galvanometer.
2. Wind both coils over a non-conducting hollow cylindrical roll.
3. Plug in the key in Coil 1: the galvanometer needle in Coil 2 deflects momentarily to one side and returns to zero.
4. Keep current steady: galvanometer shows zero deflection.
5. Unplug the key in Coil 1: the galvanometer deflects momentarily in the opposite direction.
6. Conclusion: A changing current in Coil 1 changes the surrounding magnetic field lines, inducing an electric current in neighbouring Coil 2.

(a) DC Electric Motor:

• Principle: A current-carrying coil placed in a magnetic field experiences a mechanical torque (Fleming's left-hand rule).
• Construction: Armature coil $ABCD$, strong field magnet, split rings $P$ and $Q$ (commutator), and stationary carbon brushes $X$ and $Y$.
• Working: Current passes along $A \to B$ and $C \to D$. By Fleming's left-hand rule, arm $AB$ is pushed down and arm $CD$ is pushed up, turning the coil half a turn. Commutator segments swap brush contact, reversing the current in both arms and sustaining rotation in the same direction.
• Commercial improvements: Soft iron core (armature), electromagnet instead of permanent magnet, large number of coil turns.

(a) AC Electric Generator:

• Principle: Electromagnetic induction (Faraday's law). Mechanical rotation of a coil in a magnetic field induces alternating EMF (Fleming's right-hand rule).
• Construction: Rectangular coil $ABCD$, strong magnetic poles, two complete metallic slip rings ($R_1, R_2$), and sliding carbon brushes ($B_1, B_2$).
• Working: When rotated clockwise, $AB$ moves up and $CD$ moves down. Induced current flows $A \to B \to C \to D$. After half a rotation, $CD$ moves up and $AB$ down, reversing the induced current direction to $D \to C \to B \to A$. An alternating current (AC) is delivered to the load.
• Slip rings function: Maintain continuous electrical connection with the same respective ends of the coil without reversing contacts.

(a) Field line patterns:

• Straight wire: Concentric circles around the wire.
• Circular coil: Concentric circles near wire, expanding to parallel straight lines at the centre.
• Solenoid: Uniform parallel straight lines inside, loop pattern outside identical to a bar magnet.

(b) Right-Hand Thumb Rule: Point right thumb in current direction; curled fingers show field line direction.

(c) Solenoid vs Bar Magnet: Field patterns are identical, but solenoid magnetism is temporary and strength is adjustable.

(d) Polarity of Solenoid (Clock Face Rule): Looking at an end face, if current flows clockwise it is a South pole; if anticlockwise, it is a North pole.

(a) Domestic Circuit: Current enters through Live ($220\text{ V}$) and Neutral ($0\text{ V}$) wires, passes through electricity meter, main switch, and distribution board with separate $5\text{ A}$ (lights/fans) and $15\text{ A}$ (heaters/ACs) circuits in parallel.

(b) Fuses in Live wire: When the fuse melts, it disconnects the high-voltage live supply, leaving appliances at safe zero potential.

(c) Two precautions: (1) Never touch electrical switches with wet hands, (2) Always ensure proper earthing for metal-bodied appliances.

(d) If $5\text{ A}$ fuse is replaced by $15\text{ A}$ fuse: The circuit carrying $8\text{ A}$ will not blow the $15\text{ A}$ fuse. The wires designed for $5\text{ A}$ will severely overheat ($H = I^2Rt$), melting the insulation and causing an electrical fire.

(a) Activity: Suspend an aluminium rod $AB$ between the poles of a horseshoe magnet and pass current. The rod deflects sideways, demonstrating mechanical force.

Fleming's Left-Hand Rule: Forefinger = Field, Middle finger = Current, Thumb = Force/Motion.

(b)(i) Current doubled: Force is doubled ($F \propto I$).
(ii) Parallel to field: Force is zero ($F = BIL\sin 0° = 0$).

(c) Electron beam deflection: Electrons move back to front $\implies$ conventional current $I$ is front to back. Deflection (Force $F$) is to the right. Applying Fleming's left-hand rule: Forefinger (Magnetic Field $B$) points vertically downwards.

(a) Electromagnetic Induction: Phenomenon of generating induced EMF and current by changing magnetic flux linked with a circuit.

(b) Observations with solenoid:

• Pushed in slowly: Galvanometer shows a small deflection.
• Pushed in rapidly: Galvanometer shows a much larger deflection (higher rate of change of flux).
• Reversed (South pole first): Galvanometer deflects in the opposite direction.
• Held still inside: Deflection is zero (no change in flux).

(c) Faraday's Law: The magnitude of induced electromotive force in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit.

(a) Motor vs Generator:

1. Motor converts electrical $\to$ mechanical energy; Generator converts mechanical $\to$ electrical energy.
2. Motor operates on Fleming's Left-Hand Rule; Generator operates on Fleming's Right-Hand Rule.
3. Motor uses split ring commutator; AC generator uses slip rings.

(b) Applications: Motors: electric fans, mixers, pumps. Generators: hydroelectric power stations, diesel generators, bicycle dynamos.

(c) Numerical calculation:
Power $P = 2\text{ kW} = 2000\text{ W}$, Mass $m = 100\text{ kg}$, Time $t = 1\text{ min} = 60\text{ s}$, $g = 10\text{ m/s}^2$.
Work done $W = P \times t = 2000 \times 60 = 120,000\text{ J}$.
$mgh = 120,000 \implies 100 \times 10 \times h = 120,000 \implies 1000h = 120,000 \implies \mathbf{h = 120\text{ m}}$.

(a) DC Electric Motor: Principle: A magnetic field exerts mechanical force on a current-carrying coil ($F = BIL\sin\theta$). Construction: Armature coil, strong permanent magnet, split rings (commutator), and carbon brushes.

(b) Soft iron core function: It increases the magnetic flux through the coil due to high magnetic permeability, thereby dramatically increasing the rotational torque.

(c) Energy conversion: Electrical energy $ o$ Mechanical energy.

(d) Role of split ring commutator: Swaps connections between coil and brushes every half turn ($180°$), reversing current in the coil arms so the rotational torque continues in the same angular direction.

(e) Practical applications: Electric fans, drills, washing machines, electric vehicles.