Chapter 16, Problem 72GP

To determine

The net torque on the system of rod plus charges.

Answer to Problem 72GP

The net torque on the system of rod plus charges is $\tau =QEL$ .

Explanation of Solution

Given info:

Two point charge are $+Q$ and $-Q$ .

Mass is $m$ .

Length of the rod is $L$ .

The uniform electric field is $E$ .

Formula used:

The electrostatic force acting on the 2 charges is,

  $F_E=QE$

Calculation:

The distance of each charge from the pivot point is $\frac{L}{2}$ .

The torque caused by each force will be as follows.

  $\begin{array}{c}\tau =F_E\times \frac{L}{2}\\ =\frac{QEL}{2}\end{array}$

Both the torques will tend to rotate the rod counterclockwise.

So, the net torque or moment of the couple will be ass follows.

  $\begin{array}{c}\tau =2\left(\frac{QEL}{2}\right)\\ =QEL\end{array}$

Conclusion:

Thus, the net torque on the system of rod plus charges is $\tau =QEL$ .