Question

A conducting rod AC of length $4l$ is rotated about a point 0 in a uniform magnetic field field $\overrightarrow{B}$ directed into the paper. $AO=l$ and $OC=3l$ , then

• A. $V_A-V_0=\frac{B\omega l^2}{2}$
  
• B. $V_0-V_C=\frac{7B\omega l^2}{2}$
  
• C. $V_C-V_0=\frac{9B\omega l^2}{2}$
  
• D. $V_A-V_C=4B\omega l^2$

Answer 1

The correct option is D $V_A-V_C=4B\omega l^2$

$V_0-V_A=\frac{1}{2}B{l}^{2}w$ -------(1)
$V_0-V_c=\frac{1}{2}B(3l{)}^{2}w$
$V_0-V_c=\frac{9}{2}B{l}^{2}w$ -------(2)
$\left(2\right)–\left(1\right)V_A-V_C=(\frac{9}{2}-\frac{1}{2})B{l}^{2}w$
$=\frac{8}{2}B{l}^{2}w$
$V_A-V_C=4B{l}^{2}w$