Solveeit Logo
Login

Question

Physics Question on Moving charges and magnetism

Two indentical magnetic dipoles of magnetic moment 1.0 Am21.0 \,Am^2 each, placed at a separation of 2 m2 \,m with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipoles is

A

5×10−7T\sqrt{5}\times10^{-7}T

B

5×10−7T5\times 10^{-7} T

C

10−7T10^{-7} T

D

2×10−7T2 \times 10^{-7} T

Answer

5×10−7T\sqrt{5}\times10^{-7}T

Explanation

Solution

As the axes are perpendicular, mid point lies on axial line of one magnet and on equitorial line of other magnet
∴B1=μ04π2Md3\therefore B_{1} =\frac{\mu_{0}}{4 \pi} \frac{2 M}{d^{3}}
=10−7×2×113=\frac{10^{-7} \times 2 \times 1}{1^{3}}
=2×10−7T=2 \times 10^{-7} T
and B2=μ04πMd3B_{2} =\frac{\mu_{0}}{4 \pi} \frac{M}{d^{3}}
=10−7×113=\frac{10^{-7} \times 1}{1^{3}}
=10−7T=10^{-7} T
As B1⊥B2B_{1} \perp B_{2}
∴\therefore Resultant magnetic field
=B12+B22=5×10−7T=\sqrt{B_{1}^{2}}+B_{2}^{2}=\sqrt{5} \times 10^{-7} T