A uniform magnetic field B exists in a cylindrical region of radius 10 cm as shown in. A uniform wire of length 80 cm and resistance 4.0 Omega is bent into a square frame and is 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.

Explanation

Here r=10cm, r=4 Omega`
`(dB)/(dt)=0.010T//s, (d phi)/(dt)=(dB)/(dt)A`
`e=(d phi)/(dt)=(dB)/(dt)xxA=0.01((pi xxr^2)/(2))`
`=(0.01xx3.14xx0.01)/(2)`
`=(314)/2 xx10^(-4)=1.57xx10^(-4)`
`i=e/R=(1.57/10^(-4)/(4)`
`=0.39xx10^(-4)`
`=3.9xx10^(-5)A.`