Question

Figure shows two small identical magnetic dipoles $a$ and $b$ of magnetic moments $M$ each, placed at a separation $2 d$, 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)

$B_{1}=\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}}$
$B_{2}=\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}}$
$B_{\text {net }}=\sqrt{B_{1}^{2}+B_{2}^{2}}$
$=\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}} \sqrt{5}$