Question

Two identical magnetic dipoles of magnetic moment $2A{m}^2$ are placed at a separation of $2m$ with their axes perpendicular to each other in air. The resultant magnetic field at a midpoint between the dipoles is

• A. $4\sqrt{5}\times {10}^{-5}$T
• B. $2\sqrt{5}\times {10}^{-5}$T
• C. $4\sqrt{5}\times {10}^{-7}$T
• D. $2\sqrt{5}\times {10}^{-7}$T

Answer 1

The correct option is D $2\sqrt{5}\times {10}^{-7}$T

Let point P be a midpoint between the dipoles. The point P will be in end-on position with respect to one dipole and in broad-side on position with respect to the other.

$\therefore B_1=\frac{{\mu }_0}{4\pi }\frac{2m}{r_1^3}=\frac{{10}^{-7}\times 2\times 2}{(1{)}^3}=4\times {10}^{-7}T$

and $B_2=\frac{{\mu }_0}{4\pi }\frac{m_2}{r_2^3}=\frac{{10}^{-7}\times 2}{(1{)}^3}=2\times {10}^{-7}T$

As $B_1$ and $B_2$ are perpendicular to each other, therefore the resultant magnetic field at point P is

$B=\sqrt{B_1^2+B_2^2}$

$B=2\sqrt{5}\times {10}^{-7}T$