Question

Two identical magnetic dipoles are placed, as shown separated by distance $d$. The magnetic field, mid way between the dipoles, is :

• A. $\frac{{\mu }_{0}M\sqrt{2}}{4\pi d^3}$
• B. $\frac{{\mu }_{0}M\sqrt{5}}{4\pi d^3}$
• C. $\frac{2{\mu }_{0}M\sqrt{5}}{\pi d^3}$
• D. none of these

Answer 1

Answer: (C)

$\frac{2{\mu }_{0}M\sqrt{5}}{\pi d^3}$

$B=\sqrt{B_1^2+B_2^2}$
$=\frac{{\mu }_{0}M}{4\pi (\frac{d}{2}{)}^3}\sqrt{1^2+2^2}=\frac{2{\mu }_{0}M\sqrt{5}}{\pi d^3}$