A uniform magnetic field B exists in a direction perpendicular to the plane of a square frame made of copper wire. The wire has a diameter of 2 mm and a total length of 40cm. The magntic field changes with time at a steady rate `(dB)/dt = 0.02 T s ^(-1)`. Find the current induced in the frame. Resistivity of copper `=1.7 X 10 ^(-8) Wm`.

Explanation

Area of frame, `A = ((40)/(4) xx 10^(-2) m)^(2) = 10^(-2) m^(2)`
`e = (d phi)/(dt) = A (db)/(dt) = 10^(2) xx 0.02 = 2 xx 10^(-4) V`
Resistance of loop, `R = (rho l)/(a) = (rho l)/(pi r^(2))`
`R = (1.7 xx 10^(-8) xx 40 xx 10^(-2))/((22)/(7) xx (10^(-3))^(2)) = 2.16 xx 10^(-3) ohm`
Induced current, `i = (e)/(R ) = (2 xx 10^(-4))/(2.16 xx 10^(-3))`
`= 9.3 xx 10^(-2) A`