A coil consisting of 50 turns is placed in a region of changing magnetic field. If the mag… — JAMB UTME

A coil consisting of $50$ turns is placed in a region of changing magnetic field. If the magnetic flux passing through the coil increases uniformly from $0.2\text{ Wb}$ to $0.6\text{ Wb}$ in $2.0\text{ s}$ , what is the magnitude of the induced electromotive force in the coil in volts?

Answer: 10 V

Answer

The magnitude of the induced electromotive force in the coil is

10\text{ V}

According to Faraday's law of electromagnetic induction, the magnitude of the induced electromotive force

E

is proportional to the number of turns

N

and the rate of change of magnetic flux

\frac{\Delta \Phi}{\Delta t}

. Given

N = 50

\Delta \Phi = 0.6\text{ Wb} - 0.2\text{ Wb} = 0.4\text{ Wb}

, and

\Delta t = 2.0\text{ s}

, substituting these into

E = N \frac{\Delta \Phi}{\Delta t}

gives

E = 50 \times \frac{0.4}{2.0} = 10\text{ V}

Step-by-Step Solution

Determine the change in magnetic flux through the coil

\Delta \Phi = 0.6\text{ Wb} - 0.2\text{ Wb} = 0.4\text{ Wb}

Induction depends on the change in magnetic flux over time.

Apply Faraday's law of electromagnetic induction to solve for the induced e.m.f.

E = N \frac{\Delta \Phi}{\Delta t} = 50 \times \frac{0.4\text{ Wb}}{2.0\text{ s}} = 10\text{ V}

Faraday's law states that the induced e.m.f. is equal to the product of the number of turns and the rate of change of flux.

Key Concept

Faraday's Law of Electromagnetic Induction

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