Question

Two indentical magnetic dipoles of magnetic moment $1.0 \,Am^2$ each, placed at a separation of $2 \,m$ with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is

• A. $\sqrt{5}\times10^{-7}T$
• B. $5\times 10^{-7} T$
• C. $10^{-7} T$
• D. $2 \times 10^{-7} T$

Answer 1

The Correct Option is A

As the axes are perpendicular, mid point lies on axial line of one magnet and on equitorial line of other magnet
$\therefore B_{1} =\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}} $
$=\frac{10^{-7} \times 2 \times 1}{1^{3}} $
$=2 \times 10^{-7} T$
and $B_{2} =\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}} $
$=\frac{10^{-7} \times 1}{1^{3}} $
$=10^{-7} T$
As $B_{1} \perp B_{2}$
$\therefore$ Resultant magnetic field
$=\sqrt{B_{1}^{2}}+B_{2}^{2}=\sqrt{5} \times 10^{-7} T$