question_answer

A rectangular loop of side 6 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.4 T directed normal to the loop. The voltage developed across the cut if velocity of loop is \[2\text{ }cm\text{ }{{s}^{-1}}\] in a direction normal to the longer side is:

A) \[3.8\times {{10}^{-4}}V\]                   

B) \[4.8\times {{10}^{-4}}V\]

C) \[2.2\times {{10}^{-2}}V\]                   

D) \[3.2\times {{10}^{-2}}V\]

Correct Answer: B

Solution :

(b) \[4.8\times {{10}^{-4}}V\] Here,   \[l=6\,cm=6\times {{10}^{-2}}m\]             \[B=0.4\,T,\]             \[v=2\times {{10}^{-2}}m{{s}^{-1}}\] Voltage developed is             \[\varepsilon =Blv\]             \[=0.4\times 6\times {{10}^{-2}}\times 2\times {{10}^{-2}}\]             \[=4.8\times {{10}^{-4}}V\]