question_answer

The magnetic Held at a distance r from a long wire carrying current i is 0.4 T. The magnetic field at a distance 2 r is :

A)  0.2T           

B)  0.8 T

C)  0.1 T           

D)  1.6 T

Correct Answer: A

Solution :

 Magnetic field [b] due to current carrying wire at a distance r is \[B=\frac{{{\mu }_{0}}}{2\,\pi }\frac{i}{r}\] \[\Rightarrow \] \[\frac{{{B}_{1}}}{{{B}_{2}}}=\frac{{{r}_{2}}}{{{r}_{1}}}\] \[\Rightarrow \] \[{{B}_{2}}=\frac{{{r}_{1}}}{{{r}_{2}}}{{B}_{1}}\] Given, \[{{r}_{1}}={{r}_{2}},\,\,{{r}_{2}}=2r,\,\,{{B}_{1}}=0.4\,T\] \[\therefore \] \[{{B}_{2}}=\frac{r}{2\,r}\times 0.4=0.2\,T\]