Question

A hypothetical magnetic field existing in a region is given by $\overrightarrow{B}=B_0{\overrightarrow{e}}_r$, where ${\overrightarrow{e}}_r$ denotes the unit vector along the radial direction. A circular loop of radius $\alpha ,$ carrying a current $i$, is placed with its plane parallel to $X-Y$ plane and the centre at $(0,0,d)$. Find the magnitude of the magnetic force acting on the loop.

• A. $\frac{i2\pi b_o{a}^3}{\sqrt{a^2+d^4}}$
  
• B. $\frac{i2d_o{a}^2}{\sqrt{a^2+b^2}}$
• C. $\frac{\pi b_o{a}^2}{\sqrt{a+d^2}}$
• D. $\frac{i2\pi b_o{a}^2}{\sqrt{a^2+d^2}}$

Answer 1

The correct option is D $\frac{i2\pi b_o{a}^2}{\sqrt{a^2+d^2}}$

$\overrightarrow{B}=B_0\overrightarrow{e_r}$

$\overrightarrow{e_r}$= unit vector along radial direction

$F=i(\overrightarrow{l}\times \overrightarrow{B})=iIB\sin \theta$

$F=\frac{i\left(2\pi a\right)B_{0}a}{\sqrt{a^2+d^2}}=\frac{i2\pi a^2{B}_0}{\sqrt{a^2+d^2}}$