Question

Two identical short magnetic dipoles of magnetic moments $1.0{\text{Am}}^2$ each, placed at a separation of $2\text{m}$ , with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipole is-

• A. $5\times {10}^{-7}\text{T}$
• B. $\sqrt{5}\times {10}^{-7}\text{T}$
• C. ${10}^{-7}\text{T}$
• D. $2\times {10}^{-7}\text{T}$

Answer 1

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


Fields due to the magnetic dipole moments are,

$B_1=\frac{{\mu }_0\left(2M\right)}{4\pi (d{)}^3}$

$=\frac{2{\mu }_0\times 1}{4\pi \times 1^3}=(\frac{2{\mu }_0}{4\pi })\text{T}$

$B_2=\frac{{\mu }_0\left(M\right)}{4\pi (1{)}^3}=\frac{{\mu }_0\times 1}{4\pi \times 1}=(\frac{{\mu }_0}{4\pi })\text{T}$

The net magnetic field is,

$B=\frac{{\mu }_0}{4\pi }\sqrt{1^2+2^2}$

$B=\frac{\sqrt{5}{\mu }_0}{4\pi }=\sqrt{5}\times {10}^{-7}\text{T}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.