Question

A circular coil having mass $m$ is kept above the ground (x–z plane) at some height. The coil carries a current $i$ in the direction shown in figure. In which direction a uniform magnetic field $B$ should be applied so that the magnetic force balances the weight of the coil?

• A. x. direction
• B. y-direction
• C. z-direction
• D. None of these

Answer 1

The correct option is D None of these

Let us consider the case where there is a uniform magnetic field $\overrightarrow{B}$ in the x-direction.
Consider the top view of the circular coil with two diametrically opposite current elements.


Force on a current carrying element $\overrightarrow{dl}$ due to a magnetic field $\overrightarrow{B}$ is given by
$\overrightarrow{F}=i(\overrightarrow{dl}\times \overrightarrow{B})$

Thus, forces on the two elements will also be opposite to each other.


Similarly for each pair of diametrically opposite current elements, the forces will be equal and opposite in direction. Hence, the net magnetic force acting on the loop will be zero.


Similarily, if we have a uniform magnetic field along the y or z directions, we will have the same outcome because the forces on diametrically opposite elements will cancel each other. In none of the cases, the force due to magnetic field will balance the weight of the coil. Hence the correct option is (d).