Question

There is a square loop of side $l=10\text{cm}$. The resistance of loop is $0.5\Omega /\text{cm}$. The loop is moved with constant velocity $2\hat{i}\text{m/s}$ in two uniform magnetic field as shown in the figure. The magnitude of magentic field is $10\text{T}$ in both regions. Then

• A. The potential difference across the points $CD$ is zero
• B. The potential difference across the points $AC$ is $2\text{V}$
• C. Current through the loop is $20\text{A}$
• D. Current through the loop is $10\text{A}$

Answer 1

Answer: (A), (B), (C)

Current through the loop is $20\text{A}$

As length is parallel to velocity for sides $CD$ and $AB$, emf generated in these sides is $0$

For Side $BC,$ emf generated is $Blv=10\left(0.1\right)2=2\text{V}$
Potential difference across $AC$ is $2+0=2\text{V}$

For Side $AD,$ emf generated is $Blv=10\left(0.1\right)2=2\text{V}$

Net potential in the loop is $V=4\text{V}$
Total resistance of the loop is $0.5(4\times 0.1)=0.2\Omega$

Current through the loop is $\frac{V}{R}=20\text{A}$