Question

A 6. 9 x 106 n/c electric field balances the force of gravity on a plastic sphere with a charge of 3. 0 nc. What is the mass of the sphere?.

Answer 1

Hi there!

If the forces are balanced, we know that:

`\Sigma F = F_E - F_g = 0 \\\\F_E = F_g`

The electric field force and force due to gravity must be EQUAL.

The equation for force due to an electric field is:

`F_E = qE`

q = Charge of particle (C)
E = Electric Field Strength (N/C)

The equation for force due to gravity:

`F_g = W = Mg`

M = Mass (kg)
g = acceleration due to gravity (9.8 m/s²)

Set the two equal and solve for mass.

`qE = Mg\\\\M = (qE)/(g) = \boxed{0.0021 kg}`