Question

There is a uniform magnetic field $B$ directed in negative $z$ direction. A conductor $ABC$ has length $AB=l_1$, parallel to the $x-$axis, and length $BC=l_2$ parallel to the $y-$axis. $ABC$ moves in the $xy$ plane with velocity $v_x\hat{i}+v_y\hat{j}$. The potential difference between $A$ and $C$ is proportional to

• A. $v_x{l}_1+v_y{l}_2$
• B. $v_x{l}_2+v_y{l}_1$
• C. $v_y{l}_1-v_x{l}_2$
• D. $v_x{l}_1-v_y{l}_2$

Answer 1

The correct option is C $v_y{l}_1-v_x{l}_2$

Emf induced is due to velocity component perpendicular to the length of the conductor.
Emf induced in $AB$ is ${\epsilon }_1=B{l}_1{v}_y$ [$A$ positive]
Emf induced in $BC$ is ${\epsilon }_2=B{l}_2{v}_x$ [$C$ positive]
$\therefore {\epsilon }_{AC}=l_1{v}_y-l_2{v}_x$