Question

A rod of length $l$ is rotating about one end $\text{A}$ in a uniform magnetic field $B$ which is perpendicular to the plane of rotation of the rod. Point $\text{B}$ is the midpoint of the rod. Find the potential difference between points $\text{B}$ and $\text{C}$ if the potential difference between $\text{A}$ and $\text{C}$ is $25\text{V}.$

• A. $\frac{12}{5}\text{V}$
• B. $\frac{25}{4}\text{V}$
• C. $\frac{75}{4}\text{V}$
• D. $\frac{7}{5}\text{V}$

Answer 1

The correct option is C $\frac{75}{4}\text{V}$

Potential difference between points $\text{A}$ and $\text{C}$ is,

$V_A-V_C=25\text{V}$

Also,
$V_A-V_C=\frac{B\omega l^2}{2}$

$V_A-V_C=\frac{B\omega l^2}{2}=25\text{V}.....\left(1\right)$

Potential difference between points $\text{A}$ and mid-point $\text{B}$ is,

$V_A-V_B=\frac{B\omega {\left(\frac{l}{2}\right)}^2}{2}=\frac{1}{4}\left[\frac{B\omega l^2}{2}\right]$

$V_A-V_B=\frac{25}{4}\text{V}...........\left(2\right)$

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

$V_B-V_C=25-\frac{25}{4}$

$\therefore V_B-V_C=\frac{75}{4}\text{V}$

Hence, $\left(\text{C}\right)$ is the correct answer.