Question

A conducting circular loop of radius a and resistance R is kept on a horizontal plane. A vertical time varying magnetic field B = 2t is switched on at time t = 0. Then

• A. Flow of charge per unit time from any section of the coil is constant
• B. Total charge passed through any section between time t = 0 to t = 2 is $\left(\frac{4\pi a^2}{R}\right)$
• C. Power generated in the coil at any time t is constant R
• D. All of these

Answer 1

The correct option is D All of these

Q= B.A (As B is perpendicular to the plane of coil)

$E=-\frac{dQ}{dt}=-A\frac{dB}{dt}|E|=\pi a^2\frac{d}{dt}\left(2t\right)=2\pi a^2$

The flow of charge is current $i=\frac{2\pi a^2}{R}$ constant P.

Therfore power generated $P=i^{2}R=constant$

Charges passes $Q=\int idt={\int }_0^2\frac{2\pi a^2}{R}dtQ=\frac{2\pi a^2}{R}{\left[t\right]}_0^2=\frac{4\pi a^2}{R}$

Option D correct.