Question

What are the strength and direction of an electric field that will balance the weight of a 1.0 g plastic sphere that has been charged to -3.0 nC?

Short answer

The electric field that will balance the weight is$3.27\times {10}^6\mathrm{V}/\mathrm{m}$

Step-by-step solution

Given information

mass of the sphere $m=1g=0.001kg$

charge of the sphere$q=-3.0\times {10}^{-9}C$

Explanation

In order to balance the weight of the sphere, the electric force must be equal in magnitude to the weight of the sphere: $F_E=qE=mg$

Solving the equation for E, we find the strength of the electric field:

$E=\frac{mg}{q}=\frac{\left(0.001\mathrm{kg}\right)\left(9.81\mathrm{m}/{\mathrm{s}}^2\right)}{3.0\times {10}^{-9}\mathrm{C}}=3.27\times {10}^6\mathrm{V}/\mathrm{m}$