A wire loop of radius 10 cm has a resistance of 2.0 $\varOmega$.The loop is at right angles to a uniform magnetic field B. The field strength is changing at a rate of $\Delta$B/$\Delta$t = 0.10 T/s.What is the magnitude of the induced current in the loop?
A)0.3 mA
B)1.0 mA
C)1.6 mA
D)2.9 mA

Question

Quizplus · Accepted Answer

The induced EMF in the loop is given by:
EMF = -N(dΦ/dt)
where N is the number of turns in the loop and Φ is the magnetic flux through the loop. Since the loop is perpendicular to the magnetic field, the magnetic flux is given by Φ = πr^2B, where r is the radius of the loop and B is the magnetic field strength.

So, EMF = -N(πr^2)(dB/dt)

The induced current in the loop is given by:
I = EMF/R
where R is the resistance of the loop.

Substituting the given values, we get:

EMF = -N(πr^2)(dB/dt) = -(1)(π(0.1)^2)(0.10) = -0.00314 V

I = EMF/R = (-0.00314)/(2.0) = -0.00157 A = 1.57 mA

Since the current is induced in the opposite direction to the change in magnetic field, the magnitude of the induced current is 1.57 mA or 1.6 mA (rounded to the nearest tenth). Therefore, the best choice is C.

A Wire Loop of Radius 10 Cm Has a Resistance Ω\varOmegaΩ

A Wire Loop of Radius 10 Cm Has a Resistance $\varOmega$