Question

A uniform magnetic field B exists in a cylindrical region of radius 10 cm as shown in figure. A uniform vire of length 80 cm and resistance 4.0 $Omega$ is bent into a square frame and id placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of 0.010 T/s, find the current induced in the frame.

Answer 1

Here r = 10~cm, R = $4\Omega$

e = $\frac{d\Phi }{dt}=\frac{dB}{dt}\times A=0.01\left(\frac{n\times r^2}{2}\right)$

= $\frac{0.01\times 3.14\times 0.01}{2}$

= $\frac{3.14}{2}\times {10}^{-4}=1.57\times {10}^{-4}$

i = $\frac{e}{R}=\frac{1.57\times {10}^{-4}}{4}$

= $0.39\times {10}^{-4}$

= $3.9\times {10}^{5}A$