Question #42972

The primary circuit of a potentiometer lies in the plane of the paper and consists of a DC battery of constant EMF $V_0 = 10 \text{ V}$ and negligible internal resistance. It is connected in series with a conducting circular loop of area $A = 0.1 \text{ m}^2$ and resistance $R_L = 5 \ \Omega$, and a uniform potentiometer wire $AB$ of length $L = 1 \text{ m}$ and resistance $R_w = 5 \ \Omega$. The battery drives a clockwise current through the loop. A uniform magnetic field $B$, localized to the region of the loop and directed into the paper, varies with time $t$ as $B(t) = 5 t^2 \text{ T}$. A secondary circuit containing a standard cell of EMF $E_s = 2.88 \text{ V}$ and a galvanometer is connected between point $A$ and a jockey to find the null point $x$ on the wire $AB$. Taking the direction from $A$ to $B$ as positive, what is the velocity of the null point at $t = 2 \text{ s}$?