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

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

Step-by-step 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=-(d\phi)/(dt)`

Ohm's law is :

`\epsilon=IR`

So,

`IR=-(d\phi)/(dt)\\\\IR=-(d(NBA))/(dt)\\\\IR=-NA(dB)/(dt)\\\\(dB)/(dt)=(IR)/(NA)\\\\(dB)/(dt)=(0.05* 12.4)/(104* 7.2* 10^(-2)* 3.7* 10^(-2))\\\\(dB)/(dt)=2.23\ T/s`

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