Question

What is the strength of an electric field that will balance the weight of a 3.3 g plastic sphere that has been charged to -7.6 nc ?

Answer 1

As the plastic sphere is charged, therefore it experience an electric force when placed in an electric fields and also experiences gravitational force acts downward so the electric force must act upward.

Let  $F_{E}$ is electric force and $F_{G}$ is gravitational force.

If these forces are balanced, therefore$F_{E} = F_{G}$

or                                                                      $\left | q \right |E=mg\\\\\ E=\frac{mg}{\left | q \right |}$

Given, $q=-7.6 nC=-7.6\times10^{-9} C$ and  $m=3.3 g= 3.3\times10^{-3} kg$.

Substituting these values in above equation we get,

$E=\frac{3.3\times10^{-3} kg\times9.8 m/s^{2} }{7.6\times10^{-9} C}\\\\E=4.2\times10^{6} N/C$

Thus, the magnitude of electric field is $4.2\times10^{6} N/C$.

As the charge is negative, the electric field at the location of the plastic sphere must be pointing downward.