Question

A tiny ball (mass = 0.010 kg) carries a charge of -22uC. What is the electric field magnitude that would cause the ball to float above the ground?

Answer 1

let's assume we have a frame(X, Y). Two forces are acting on a body; i) gravity that acts downwards(y- direction).ii) Lorenz force that acts upwards(y+ direction). If we change the direction of the field the ball will fall to the ground faster. therefore the only direction that will keep the ball above the ground is Lorenz force(Y+ direction).

Newton's second law shows that:

$ma=\sum{F}=qE-g$

$qE-mg=0$ ( because the ball is in equilibrium a=0)

$E=\frac{mg}{q}=\frac{0.010\times9.81}{22}=0.00446V/m$

$=4.5\times10^{-3}V/m$