Source: High school physics (Chinese)
Problem Sets:
Problem
A small charged plastic sphere with mass $m = 3.06 \times 10^{-5}$ kg is suspended and stationary in a uniform electric field of strength $E = 6 \times 10^4$ N/C, which is directed vertically downward.
- What is the sign of the charge on the sphere?
- What is the magnitude of the charge?
The charge is negative.
$|q| = 5.00 \times 10^{-9}$ CFor the sphere to be stationary, the net force on it must be zero. The forces acting are the downward gravitational force $F_g = mg$ and the electric force $F_e = qE$. For equilibrium, the electric force must be directed upward to balance gravity.
$$F_e + F_g = 0$$Since the electric field $E$ is downward and the required electric force $F_e$ is upward, the charge $q$ must be negative. The magnitudes of the forces must be equal:
$$|F_e| = |F_g| \implies |q|E = mg$$ $$|q| = \frac{mg}{E}$$Using $g = 9.8$ m/s².