The magnetic flux through a certain coil is given by
$\phi$ _m = (1/50 $\pi$ ) cos 100 $\pi$ t
Where the units are SI. The coil has 100 turns. The magnitude of the induced EMF when t = 1/200 s is

Question

The magnetic flux through a certain coil is given by $\phi$_m = (1/50 $\pi$) cos 100 $\pi$t Where the units are SI. The coil has 100 turns. The magnitude of the induced EMF when t = 1/200 s is

Quizplus · Accepted Answer

The induced EMF can be calculated using Faraday's law of induction:

EMF = -N(dΦ/dt)

Where N is the number of turns and Φ is the magnetic flux through the coil. Taking the derivative of the given formula for Φ with respect to time, we get:

dΦ/dt = -(1/5000π)sin(100πt)

Substituting t = 1/200 s, we get:

dΦ/dt = -(1/5000π)sin(π/2) = -(1/5000π)

Substituting this value for dΦ/dt and N = 100, we get:

EMF = 100(1/5000π) = 2/π V ≈ 0.6366 V

The closest answer choice to this value is B, 200 V.

The Magnetic Flux Through a Certain Coil Is Given By \phi