Question

A styrofoam ball of mass 0.120 g is placed in an electric field of 6000 n/c pointing downward. What charge must be placed on the ball for it to be suspended?

Answer 1

Answer:

$q=-1.96\cdot 10^{-7}C$

Explanation:

In order for the ball to be suspended, the electric force on it must be equal to the weight of the ball, so we can write:

$qE=mg$

where

qE is the electric force

mg is the weight

q is the charge on the ball

E = 6000 N/C is the electric field

$m=0.120 g = 0.120 \cdot 10^{-3} kg$ is the mass of the ball

$g=9.8 m/s^2$ is the acceleration of gravity

Solving for q, we find the magnitude of the charge:

$q=\frac{mg}{E}=\frac{(0.120\cdot 10^{-3})(9.8)}{6000}=1.96\cdot 10^{-7} C$

Now we have to determine the direction. We know that:

- The weight points downward, so the electric force must acts upwnward

- The electric field points downward: so, F and E have opposite directions

- This means that the charge is negative

So, the answer is

$q=-1.96\cdot 10^{-7}C$