Question

A long, thin rod (length = 4.0 m) lies along the x axis, with its midpoint at the origin. In a vacuum, a +8.0C point charge is fixed to one end of the rod, and a -8.0C point charge is fixed to the other end. Everywhere in the x, y plane there is a constant external electric field (magnitude 8.0 × 10^3 N/C) that is perpendicular to the rod. With respect to the z axis, find the magnitude of the net torque applied to the rod.

Answer 1

256 x 10³ Nm

Step-by-step explanation:

Force on each of the charges of 8 C due to uniform electric field in x -y plane will be equal and opposite because one is positive charge and the other is negative charge. They will make a couple

Each of the forces of the couple will act in x - y plane and will be equal to

F = Q E = 8 X 8 X 10³

= 64 X 10³ N

Arm of the couple = 4 m

Moment of couple about z axis.

= 64 x 10³ x 4

= 256 x 10³ Nm.