question_answer

At the centre of a circular coil of radius 5 cm carrying current, magnetic field due to earth is \[0.5\times {{10}^{-5}}\text{ }W/{{m}^{2}}.\] What should be the current flowing through the coil so that it annuls the earth's magnetic field

A)  40 A                           

B)  4 A

C)  0.4 A                          

D)  0.2 A

Correct Answer: C

Solution :

 \[r=5cm.=5\times {{10}^{-2}}m\]\[{{B}_{E}}=0.5\times {{10}^{-5}}W/{{m}^{2}}\]we know that field due to coil at centre \[B=\frac{{{\mu }_{0}}I}{2r}\] it annuals the earth's megnetic field So, \[\frac{{{\mu }_{0}}I}{2r}=0.5\times {{10}^{-5}}\] \[I=\frac{2R\times 0.5\times {{10}^{-5}}}{\mu }=\frac{5}{4\pi }A=0.4A\]