Question

Figure shows two small identical magnetic dipoles $a$ and $b$ of magnetic moments $M$ each, placed at a separation $2d$, with their axes perpendicular to each other. The magnetic field at the point $P$ mid way between the dipoles is

• A. $\frac{2{\mu }_{0}M}{4\pi d^3}$
• B. $\frac{{\mu }_{0}M}{4\pi d^3}$
• C. Zero
• D. $\frac{\sqrt{5}{\mu }_{0}M}{4\pi d^3}$

Answer 1

Answer: (D)

$B_1=\frac{{\mu }_0}{4\pi }\frac{2M}{d^3}$
$B_2=\frac{{\mu }_0}{4\pi }\frac{M}{d^3}$
$B_{\text{net }}=\sqrt{B_1^2+B_2^2}$
$=\frac{{\mu }_0}{4\pi }\frac{M}{d^3}\sqrt{5}$