Question

Two indentical magnetic dipoles of magnetic moment $1.0A{m}^2$ 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. $\sqrt{5}\times {10}^{-7}T$
• B. $5\times {10}^{-7}T$
• C. ${10}^{-7}T$
• D. $2\times {10}^{-7}T$

Answer 1

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

Given,

Magnetic dipole of both magnet $=m_1=m_2=1.0A{m}^2$

Separation between them$=2m$

Since axes are perpendicular so mid point lies on axial line of one magnet and on equitorial line of other magnet
$\therefore B_1=\frac{{\mu }_{0}2M}{4\pi d^3}=\frac{{10}^{-7}\times 2\times 1}{1^3}=2\times {10}^{-7}T$
and $B_2=\frac{{\mu }_{0}M}{4\pi d^3}=\frac{{10}^{-7}\times 1}{1^3}={10}^{-7}T$
As $B_1\perp B_2$
$\therefore$ Resultant magnetic field
$=\sqrt{B_1^2+B_2^2}=\sqrt{5}\times {10}^{-7}T$

So the resultant magnetic field at a point midway between the dipole is $=\sqrt{5}\times {10}^{-7}T$