question_answer

In given figure, a wire loop has been bent so that it has three segments: segment ab (a quarter circle), be (a square comer), and a ca (straight). Here are three choices for a magnetic field through the loop                        

(1) \[{{\vec{B}}_{1}}=3\hat{i}+7\hat{j}-5t\hat{k}\]

(2) \[{{\vec{B}}_{2}}=5t\hat{i}-4\hat{j}-15\hat{k}\]

(3) \[{{\vec{B}}_{3}}=2\hat{i}-5t\hat{j}-12\hat{k}\]

where \[\vec{B}\] is in milliteslas and t is in seconds. If the induced current in the loop due to \[{{\vec{B}}_{1}},{{\vec{B}}_{2}}\] and \[{{\vec{B}}_{3}}\] are \[{{i}_{1}},{{i}_{2}}\] and \[{{i}_{3}}\] respectively, then

A)  \[{{i}_{1}}>{{i}_{2}}>{{i}_{3}}\]                 

B)  \[{{i}_{2}}>{{i}_{1}}>{{i}_{3}}\]

C)  \[{{i}_{3}}>{{i}_{2}}>{{i}_{1}}\]                 

D)  \[{{i}_{1}}={{i}_{2}}={{i}_{3}}\]