Question

A conducting circular ring and a conducting elliptical ring both are moving pure transnationally in a uniform magnetic field of strength B as shown in figure on a horizontal conducting pane potential difference between top most point of circle and ellipse is:

Answer 1

Given:

A conducting circular ring and a conducting elliptical ring both are moving pure transnationally in a uniform magnetic field of strength B as shown in figure on a horizontal conducting plane.

To find:

Potential difference between top most point of circle and ellipse

Calculation:

Potential difference between lowest point and highest point of ellipse:

$V_{2} - V_{1} = B(4a)(2v) \: \: \: \: .....(1)$

Potential difference between lowest point and highest point of circle:

$V_{3} - V_{4} = B(2a)v \: \: \: \: .....(2)$

Now since points 3 and 2 are located on the same conducting plane , the potential of those points will be same;

$V_{3} = V_{2} \: \: \: .......(3)$

Subtracting eq.(2) from eq.(1);

$\therefore \: (V_{2} -V_{1}) - (V_{3} - V_{4}) = 8Bav-2Bav$

$= > \: V_{2} -V_{1} - V_{3} + V_{4}= 6Bav$

$= > \: \cancel{ V_{2} }-V_{1} - \cancel{V_{3} } + V_{4}= 6Bav$

$= > V_{4} - V_{1}= 6Bav$

$= > V_{1} - V_{4}= -6Bav$

So, final answer is:

$\boxed{ \sf{ \large{V_{1} - V_{4}= -6Bav }}}$