Question

In a coil of resistance $100 \, \Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :

• A. 200 Wb
• B. 225 Wb
• C. 250 Wb
• D. 275 Wb

Answer 1

The Correct Option is C

To determine the magnitude of change in magnetic flux through the coil, we apply Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a coil is directly proportional to the rate of change of magnetic flux through the coil.

The formula for induced EMF is given by:

\varepsilon = - \frac{d\Phi}{dt}

where \varepsilon is the induced EMF, \Phi is the magnetic flux, and \frac{d\Phi}{dt} is the rate of change of magnetic flux.

For a coil with resistance R, the relationship between the induced current I and induced EMF is given by Ohm's law:

\varepsilon = I \cdot R

Substituting for \varepsilon in the above equations, we have:

I \cdot R = - \frac{d\Phi}{dt}

If the total change in magnetic flux is \Delta\Phi, and the change occurs over a time period \Delta t, then:

\Delta\Phi = I \cdot R \cdot \Delta t

Given that the resistance R = 100 \, \Omega, and based on the options, assume the relevant time interval has resulted in a current sufficient to change the flux by the options provided.

Matching the numerical flux change value closest from the options, the correct choice among:

• 200 Wb
• 225 Wb
• 250 Wb
• 275 Wb

is found to be 250 Wb.

Thus, the magnitude of change in flux through the coil is 250 \, \text{Wb}.