4.1 Force on a Current-Carrying Conductor in a Magnetic Field
When a current-carrying conductor is placed in a magnetic field, the interaction between the magnetic field of the conductor and the external magnetic field produces a catapult field (resulting magnetic field), exerting a magnetic force on the conductor.
1. Direction of Force (Fleming's Left-Hand Rule)
The direction of the magnetic force can be determined using Fleming's Left-Hand Rule:
- Thumb: Direction of Force / Motion ($F$)
- First Finger: Direction of Magnetic Field ($B$, North to South)
- Second Finger: Direction of Current ($I$, Positive to Negative)
2. Factors Affecting the Magnitude of the Magnetic Force
The magnetic force increases when:
- Current ($I$) increases.
- Strength of the permanent magnetic field ($B$) increases.
- Length ($l$) of the conductor in the magnetic field increases.
3. Turning Effect of a Current-Carrying Coil in a Magnetic Field
In a direct current (d.c.) motor, opposite sides of a rectangular coil experience forces in opposite directions, creating a turning moment (couple).
- Split-ring commutator: Reverses the current direction in the coil every half-rotation to ensure continuous rotation in one direction.
- Carbon brushes: Maintain electrical contact with the rotating commutator.
4.2 Electromagnetic Induction
Electromagnetic Induction is the production of an electromotive force (e.m.f.) across an electrical conductor in a changing magnetic field, or when a conductor cuts magnetic flux.
1. Laws of Electromagnetic Induction
- Faraday's Law: The magnitude of the induced e.m.f. is directly proportional to the rate of cutting of magnetic flux or rate of change of magnetic flux linkage.
- Lenz's Law: The induced current always flows in such a direction that it opposes the change or motion producing it (Conservation of Energy).
2. Direction of Induced Current
For a straight conductor moving across a magnetic field, use Fleming's Right-Hand Rule (Generator Rule):
- Thumb: Direction of Motion / Force ($F$)
- First Finger: Direction of Magnetic Field ($B$)
- Second Finger: Direction of Induced Current ($I$)
3. Direct Current (d.c.) vs. Alternating Current (a.c.) Generators
- d.c. Generator: Uses a split-ring commutator to produce current in one direction.
- a.c. Generator: Uses slip rings to produce current that alternates direction every half-cycle.
4.3 Transformer
A transformer changes the voltage of an alternating current (a.c.) supply through continuous mutual induction between two coils wrapped around a soft iron core.
1. Transformer Equations
For an ideal transformer (100% efficiency):
$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$
$$P_p = P_s \implies V_p I_p = V_s I_s$$
- Step-Up Transformer: $N_s > N_p \implies V_s > V_p$ and $I_s < I_p$
- Step-Down Transformer: $N_s < N_p \implies V_s < V_p$ and $I_s > I_p$
2. Efficiency of a Transformer
$$\text{Efficiency } (\eta) = \frac{\text{Output Power } (P_s)}{\text{Input Power } (P_p)} \times 100\% = \frac{V_s I_s}{V_p I_p} \times 100\%$$
3. Energy Losses in Transformers and Ways to Reduce Them
- Resistance of Coils (Joule heating): Use thick copper wires with low resistance.
- Eddy Currents in Core: Use a laminated soft iron core insulated with lacquer.
- Hysteresis Loss (Magnetisation/Demagnetisation): Use a soft iron core which is easily magnetised and demagnetised.
- Flux Leakage: Wind the secondary coil directly over the primary coil.
4.4 Generation and Transmission of Electricity
1. National Grid Network Systems
Electricity generated at power stations ($\approx 11\text{ kV} - 25\text{ kV}$) is stepped up to ultra-high voltages ($132\text{ kV}, 275\text{ kV}, 500\text{ kV}$) for long-distance transmission.
2. Power Loss in Transmission Cables
Power lost as heat in transmission cables of resistance $R$ carrying current $I$:
$$P_{\text{loss}} = I^2 R$$
Stepping up the voltage $V$ reduces the current $I$ ($I = \frac{P}{V}$), which significantly lowers power loss ($P_{\text{loss}} \propto I^2$).