As shown in figure, a rectangular loop of length ' a' and width ' $b$ ' and made of a conducting material of uniform crosssection is kept in a horizontal plane where a uniform magnetic field of intensity $B$ is acting vertically downward. Resistance per unit length of the loop is $\lambda \Omega / \mathrm{m}$. If the loop is pulled with uniform velocity ' $v$ ' in horizontal direction, which of the following statement is / are true?

• Correct answer
  A

  Current in the loop $\mathrm{I}=\frac{\mathrm{Bbv}}{\lambda(2 \mathrm{~b}+2 \mathrm{a})}$
• B

  Current will be in clockwise direction, looking from the top.
• C

  $V_P-V_S=V_Q-V_R$, where $V$ is the potential
• Correct answer
  D

  There cannot be any induction in part SR.

Solution

$\varepsilon=B \times b \times v$ $\mathrm{i}=\frac{\varepsilon}{\mathrm{R}_{\text {total }}}=\frac{\varepsilon}{\lambda(2 \mathrm{~b}+2 \mathrm{a})}$ Current is anticlockwise $$ V_P-V_S \neq V_Q-V_R $$ Also SR, $\vec{\ell} \| \vec{v} ;$ So $\varepsilon=0$

Hence, the correct answer is options: 'A', 'D'.