A long, thin rod (length = 4.0 m) lies along the x axis, with its midpoint at the origin. In a vacuum, a +5.0 µC point charge is fixed to one end of the rod, while a -5.0 µC point charge is fixed to the other end. Everywhere in the x, y plane there is a constant external electric field (magnitude = 5.00 103 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.

Question

A long, thin rod (length = 4.0 m) lies along the x axis, with its midpoint at the origin. In a vacuum, a +5.0 µC point charge is fixed to one end of the rod, while a -5.0 µC point charge is fixed to the other end. Everywhere in the x, y plane there is a constant external electric field (magnitude = 5.00  103 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.

Damon · Answer

force on each = Q E = 5 *10^-6 * 5 * 10^3 = 25 * 10^-3 N torque resulting from each = F D = 25 * 10^-3 * 2 = 50 * 10^-3 Nm both give same sign torque so total torque = 100 *10^-3 Nm = 0.1 Nm