Physics 2009 JAMB Past Questions - Question 42: A band of 500 rectangular loops of wire of are 20 cm of 20cm , enclosed a region of magnetic field which changes from 1.0T to 0.4 T within 5 seconds, calculate the induced e.m.f.

Correct Answer

D

Explanation

To calculate the induced electromotive force (emf) in the rectangular wire loops, you can use Faraday's law of electromagnetic induction, which states that the emf induced in a closed loop is equal to the rate of change of magnetic flux through the loop. The formula for calculating the induced emf is:

emf = -dΦ/dt

Where:
- emf is the induced electromotive force (voltage).
- dΦ/dt is the rate of change of magnetic flux.

The magnetic flux (Φ) through each loop can be calculated as:

Φ = B * A

Where:
- Φ is the magnetic flux.
- B is the magnetic field strength.
- A is the area of the loop.

In your case, you have 500 rectangular loops of wire, and each loop has dimensions of 20 cm by 20 cm. To calculate the area (A) of each loop, you need to convert the dimensions to meters:

A = (20 cm / 100) * (20 cm / 100) = 0.2 m * 0.2 m = 0.04 m²

Now, calculate the initial and final magnetic flux for each loop:

Initial Φ (Φ_initial) = B_initial * A
Final Φ (Φ_final) = B_final * A

Where:
- B_initial is the initial magnetic field strength (1.0 T).
- B_final is the final magnetic field strength (0.4 T).
- A is the area of each loop (0.04 m²).

Now, calculate the change in magnetic flux (ΔΦ):

ΔΦ = Φ_final - Φ_initial
ΔΦ = (0.4 T * 0.04 m²) - (1.0 T * 0.04 m²)
ΔΦ = (0.016 T·m²) - (0.04 T·m²)
ΔΦ = -0.024 T·m²

Now, you have the change in magnetic flux (ΔΦ). To find the rate of change of magnetic flux (dΦ/dt), divide ΔΦ by the time interval (Δt), which is 5 seconds:

dΦ/dt = ΔΦ / Δt
dΦ/dt = (-0.024 T·m²) / (5 s)
dΦ/dt = -0.0048 V/s

So, the induced electromotive force (emf) in the wire loops is:

emf = -dΦ/dt
emf = -(-0.0048 V/s)
emf = 0.0048 V

The induced emf is 0.0048 volts, or 4.8 millivolts.