Question

Find the magnitude and direction of the force vector applied to the loop if the vector ${\overrightarrow{p}}_m$ is oriented along the radius vector $\overrightarrow{r}$.

• A. $\overrightarrow{F}=-\frac{{\mu }_{0}I{p}_m}{2\pi r^2}$; $\overrightarrow{F}\uparrow \downarrow \overrightarrow{B}$
• B. $\overrightarrow{F}=-\frac{{\mu }_{0}I{p}_m}{\pi r^2}$
• C. $\overrightarrow{F}=-\frac{2{\mu }_{0}I{p}_m}{\pi r^2}$
• D. $\overrightarrow{F}=-\frac{3{\mu }_{0}I{p}_m}{2\pi r^2}$

Answer 1

The correct option is A $\overrightarrow{F}=-\frac{{\mu }_{0}I{p}_m}{2\pi r^2}$; $\overrightarrow{F}\uparrow \downarrow \overrightarrow{B}$

Force on the loop is $F=p_m(\frac{\partial }{\partial \varphi }+\frac{\partial }{\partial r})\left(\frac{{\mu }_{0}i}{2\pi r}\right)=\frac{{\mu }_{0}i{p}_m}{2\pi r^2}$
The differentiation wrt $\varphi$ is zero since B has no azimuthal dependency.