question_answer

The distance between the poles of a horse shoe magnet is 0.1 m and its pole strength is 0.01 A-m. The induction of magnetic field at a point mid way between the poles will be

A)  Zero          

B)  \[2\times {{10}^{-5}}T\]

C)  \[4\times {{10}^{-6}}T\]

D)  \[8\times {{10}^{-7}}T\]

Correct Answer: D

Solution :

Net magnetic field at mid point O                 \[{{B}_{net}}={{B}_{N}}+{{B}_{S}}\] where, \[{{B}_{N}}=\] magnitude of magnetic field due to N-pole and \[{{B}_{S}}=\] magnitude of magnetic field due to S-pole But,        \[{{B}_{N}}={{B}_{S}}=\frac{{{\mu }_{0}}}{4\pi }=\frac{m}{{{r}^{2}}}\]                 \[=\frac{4\pi \times {{10}^{-7}}\times 0.01}{4\pi \times {{\left( \frac{0.1}{2} \right)}^{2}}}=4\times {{10}^{-7}}T\] \[\therefore \] \[{{B}_{net}}=8\times {{10}^{-7}}T\]