Question

The distance between the poles of horse shoe magnet is $10 \,cm$ and its pole strength is $ 10^{4} $ A. The magnetic field induction at point $P$ mid-way between the poles is :

• A. $ 8\times 10^{-9} $ tesla
• B. $ 4\times 10^{-19} $ tesla
• C. $ 2\times 10^{-9} $ tesla
• D. zero

Answer 1

Answer: (A)

$B=B_{1}+B_{2}=\frac{\mu_{0}}{4 \pi}\left(\frac{m_{1}}{r_{1}^{2}}+\frac{m_{2}}{r_{2}^{2}}\right)$
as $m_{1}=m_{2}$ and $r_{1}=r_{2}$
so, $B =\frac{\mu_{0}}{4 \pi} \frac{2 m_{1}}{r_{1}^{2}}$
$=10^{-7} \frac{2 \times 10^{-4}}{\left(5 \times 10^{-2}\right)^{2}} $
$=8 \times 10^{-9} T$