A rectangular coil of 200 turns has dimensions 0.15\text{ m} by 0.10\text{ m}. The coil is… — JAMB UTME

A rectangular coil of $200$ turns has dimensions $0.15\text{ m}$ by $0.10\text{ m}$ . The coil is placed with its plane perpendicular to a uniform magnetic field of $0.40\text{ T}$ . If the direction of the magnetic field is completely reversed in a time interval of $0.06\text{ s}$ , calculate the magnitude of the average electromotive force (e.m.f.) induced in the coil in volts.

Answer: 40 V

Answer

The magnitude of the average induced electromotive force is

40\text{ V}

According to Faraday's law of electromagnetic induction, the magnitude of induced electromotive force (e.m.f.) is given by

\mathcal{E} = N \left| \frac{\Delta \Phi}{\Delta t} \right|

. Since the coil is initially perpendicular to the magnetic field

B

, the initial flux per turn is

\Phi_i = B A

. When the field is completely reversed, the final flux becomes

\Phi_f = -B A

, giving a magnitude of flux change per turn of

|\Delta \Phi| = B A - (-B A) = 2 B A

. Substituting

N = 200

A = 0.015\text{ m}^2

B = 0.40\text{ T}

, and

\Delta t = 0.06\text{ s}

gives

\mathcal{E} = 200 \times \frac{2 \times 0.40 \times 0.015}{0.06} = 40\text{ V}

Step-by-Step Solution

Calculate the cross-sectional area of the rectangular coil

A = 0.15\text{ m} \times 0.10\text{ m} = 0.015\text{ m}^2

The area is required to determine the magnetic flux passing through the coil.

Compute the initial magnetic flux per turn

\Phi_i = B A = 0.40 \times 0.015 = 0.006\text{ Wb}

Magnetic flux is defined as the product of magnetic field strength and area when perpendicular.

Calculate the change in flux per turn when the magnetic field reverses direction

|\Delta \Phi| = \Phi_i - (-\Phi_i) = 2 \Phi_i = 0.012\text{ Wb}

Reversing the field flips the direction of the flux vectors, resulting in a net change equal to twice the magnitude of the initial flux.

Apply Faraday's Law of Electromagnetic Induction to find the induced e.m.f.

\mathcal{E} = N \frac{|\Delta \Phi|}{\Delta t} = 200 \times \frac{0.012}{0.06} = 40\text{ V}

The magnitude of induced e.m.f. equals the total rate of change of magnetic flux linkage across all turns.

Key Concept

Faraday's Law of Electromagnetic Induction (Magnetic Flux Reversal)

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