Question

The plane of a rectangular coil, 7.2 cm by 3.7 cm, is perpendicular to the direction of a uniform magnetic field B. If the coil has 104 turns and a total resistance of 12.4 Ω, at what rate must the magnitude of B change to induce a current of 0.05 A in the windings of the coil? Answer in units of T/s.

Answer 1

Answer:

The rate of change of magnetic field is 2.23 T/s.              

Explanation:

Given that,

Dimension of rectangular coil is 7.2 cm by 3.7 cm.

Number of turns in the coil, N = 104

Resistance of the coil, R = 12.4 ohms

Current, I = 0.05 A

We need to find the rate of change of magnetic field in the coil. The induced emf is given by the rate of change of magnetic flux. So,

$\epsilon=-\dfrac{d\phi}{dt}$

Ohm's law is :

$\epsilon=IR$

So,

$IR=-\dfrac{d\phi}{dt}\\\\IR=-\dfrac{d(NBA)}{dt}\\\\IR=-NA\dfrac{dB}{dt}\\\\\dfrac{dB}{dt}=\dfrac{IR}{NA}\\\\\dfrac{dB}{dt}=\dfrac{0.05\times 12.4}{104\times 7.2\times 10^{-2}\times 3.7\times 10^{-2}}\\\\\dfrac{dB}{dt}=2.23\ T/s$

So, the rate of change of magnetic field is 2.23 T/s.