Question

Two spheres have identical charges and are 75 cm apart. the force between them is +0.30 n. what is the magnitude of the charge on each sphere? (let x = charge) what can you tell about the charge signs on the spheres? ______________

Answer 1

Answer:

$4.33\cdot 10^{-6}C$, charges are both positive or both negative

Explanation:

The electrostatic force between the two spheres is given by

$F=k\frac{q_1 q_2}{r^2}$

where

k is the Coulomb's constant

q1 and q2 are the charges on the two spheres

r is the distance between the centres of the two spheres

In this problem, we have

$F=+0.30 N$ is the force

$r=75 cm=0.75 m$ is the distance between the spheres

$q_1 =q_2 =q$ because the two spheres have identical charge

Solving the formula for q, we find

$q=\sqrt{\frac{Fr^2}{k}}=\sqrt{\frac{(+0.30 N)(0.75 m)^2}{9\cdot 10^9}}=4.33\cdot 10^{-6}C$

And the two charges have the same sign (so, both positive or both negative), since the sign of the force is positive (+0.30 N), so it is a repulsive force.