Question

Two conducting rods are joined together and are moving in a magnetic field of magnitude $0.5\text{T}$ as shown in the figure. The potential difference between the ends $\text{A}$ and $\text{B}$ is $\left(\text{in volt}\right)$ :
(Give the answer in integer only)

Answer 1

The effective length of the rod between points $\text{O}$ and $\text{B}$ is:

$l_{\text{eff}}=OB=\sqrt{O{A}^2+A{B}^2}$

$=\sqrt{3^2+2^2}=\sqrt{13}\text{m}$

Emf developed across ends $\text{O}$ and $\text{B}$ is,

$V_O-V_B=\frac{B\omega (l_{\text{eff}}{)}^2}{2}$

$=\frac{0.5\times 10\times (\sqrt{13}{)}^2}{2}$

$V_O-V_B=\frac{65}{2}\text{V}.........\left(1\right)$

Emf developed across rod $\text{OA}$ is,

$V_O-V_A=\frac{B\omega l^2}{2}=\frac{0.5\times 10\times 3^2}{2}$

$V_O-V_A=\frac{45}{2}\text{V}.........\left(2\right)$

Using equations $\left(1\right)$ and $\left(2\right)$, we get

$V_A-V_B=\frac{65}{2}-\frac{45}{2}=10\text{V}$

Accepted answer: $10$