Question

A thin non conducting disc of radius $R$ is rotating clockwise as shown in figure with an angular velocity $\omega$ about its central axis, which is perpendicular to its plane. Both of its surfaces carry $+ve$ charges of uniform surface charge density. Half of the disc is in a region of uniform unidirectional magnetic field parallel to the plane of disc, as shown. Then identify the correct statement:

• A. The net torque on the disc is zero
• B. The net torque on the disc is directed leftwards
• C. The net torque on the disc is directed rightwards
• D. The net torque on the disc is parallel to $B$.

Answer 1

The correct option is B The net torque on the disc is directed leftwards

The half portion of the disc is symmetrical about the horizontal line passing through its centre.

Let us take a small element on the concentric ring forming the disc. we can see that for every element there will be its mirror element (i.e) two elements present on both sides at same angle $\theta$.


As shown in the figure the direction of magnetic force experienced by both elements is perpendicularly inward $(⨂)$ and outward $(⨀)$ respectively.

Using equation of torque :

$\overrightarrow{\tau }=\overrightarrow{R}\times \overrightarrow{F}$

The direction of torque at both element is shown below,


Thus we can see that due to symmetry the vertical component of torque gets cancels out and net torque will be directed towards Left.

This will happen with set of all elements constituting half disc, hence ${\tau }_{net}$ will be directed leftwards.

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