Question

The figure shows a conducting circular loop of radius $20\text{cm}$ placed in a uniform magnetic field $1.5\text{T}$ perpendicular to the plane of the loop. A semicircular wire $OP$ is pivoted at the center $O$ and the other end touches the loop at $P$. The center $O$ and a fixed point $Q$, on the loop, are connected by a resistor of $10\Omega$. Resistance of semicircular wire and the circular loop is negligible. Find the current flowing through the resistor, if the semicircular loop is rotating with a constant angular velocity of $5\text{rad/s}$.

• A. $0.045\text{A}$
• B. $0.035\text{A}$
• C. $0.015\text{A}$
• D. $0.025\text{A}$

Answer 1

The correct option is C $0.015\text{A}$


Effective length of the semicircular wire,

$l=$ radius of the circular loop $=0.2\text{m}$

Now, EMF induced across the wire $OP$ is,

$E=\frac{B\omega l^2}{2}$

$=\frac{1.5\times 5\times {0.2}^2}{2}=0.15\text{V}$

The equivalent circuit can be drawn as shown below.


Therefore, current flowing through the resistor is,

$i=\frac{E}{R}=\frac{0.15}{10}=0.015\text{A}$

Hence, option $\left(C\right)$ is the correct answer.