Answer to Question #189952 in Electricity and Magnetism for Milena

Question

A square loop of side a=10 cm and resistance R=0.1 ohms is placed in a uniform magnetic field B whose magnitude varies with time as shown in figure 8.23

Determine by applying Len’z law the direction of the induced current for 0<t<2s and for t>2 s

Answer 1

Magnetic field $= B$

Resistance of coil, $R=0.1\space \Omega$

Length of square, $a=10\space cm=10^{-1}\space m$

Area of cross-section, $A=10^{-2}\space m^2$

Time interval, $\Delta t=2\space s$

$\Phi=BAcos\theta=B\times10^{-2}cos0\degree=10^{-2}B$

emf induced, $V$ $=-\dfrac{d\Phi}{dt}=-\dfrac{10^{-2}B}{2}$

current, $I=\dfrac{V}{R}=-\dfrac{10^{-2}B}{2}\times\dfrac{1}{0.1}=-\dfrac{10^{-1}B}{2}$

Since, the direction of magnetic field is not provided therefore the direction of induced current cannot be determined.