Question

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

Answer 1

Let's imagine that we have frame (X,Y). There are two forces acting on the body: gravity which is directed down (in Y- direction) and Lorenz force that is directed up (in Y+ direction). If we change field direction the ball will fall on the ground even faster, so the only possible direction of the Lorenz force to keep ball above the ground is Y+ direction.

According to the second Newton's law,

$\displaystyle m a = \sum F = qE - mg$ (signs here are according to the directions of the forces)

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

$\displaystyle E = \frac{mg}{q} = \frac{0.010 \cdot 9.81}{22} = 0.00446 \; \textrm{V/m} \approx 4.5 \cdot 10^{-3}\;\textrm{V/m}$.

Answer: $4.5 \cdot 10^{-3} V/m$