question_answer

    The magnetic field at the centre of a current carrying circular loop is B. If the radius of the loop is doubled, keeping the current same, the magnetic field at the centre of the loop would be

A)  \[\frac{B}{4}\]                                 

B)  \[\frac{B}{2}\] 

C)  2B                                         

D)  4B

Correct Answer: B

Solution :

                Magnetic field at the centre of current carrying loop \[B=\frac{{{\mu }_{0}}i}{2r}\]                     ?. (i) where r is the radius of loop and i the current, Given,                   \[{{r}_{2}}=2r\] \[\therefore \]  \[\frac{{{B}_{1}}}{{{B}_{2}}}=\frac{1}{r}\times \frac{2r}{1}=\frac{2}{1}\] \[\Rightarrow \]                               \[{{B}_{2}}=\frac{{{B}_{1}}}{2}=\frac{B}{2}\] Hence, magnetic field is halved.