Question

In figure, $R$ is a fixed conducting ring of negligible resistance and radius $a$. It is hinged at the center of the ring and rotated about this point in clockwise direction with a uniform angular velocity $\omega$. There is a uniform magnetic field of strength $B$ pointing inward and $r$ is a stationary resistance. Then

• A. current through $r$ is zero
• B. current through $r$ is $\left(2B\omega a^2\right)/5r$
• C. direction of current in external resistance $r$ is from center to circumference
• D. direction of current in external resistance $r$ is from circumference to center
• E. answer required

Answer 1

Answer: (B), (D)

The correct options are
B current through $r$ is $\left(2B\omega a^2\right)/5r$
D direction of current in external resistance $r$ is from circumference to center

Current through $r=I=\frac{e}{r}$$=\frac{inducedemf}{Resistance}$
$e=-\frac{d\varphi }{dt}=-\frac{d}{dt}BAcos\theta$
$e=\frac{2Bw{a}^2}{5}$
A $=$ area swept in unit time.
$A=\frac{2w{a}^2}{5}$ (area of sector )
$\therefore I=\frac{2Bw{a}^2}{5r}$
Since the $\overrightarrow{B}$ is into the plane of the plane, the direction of current is external resistance'r' is from centre to circumference.