Question

Two small, positively charged spheres have a combined charge of 5.0 x 10 -5 C. If each sphere is repelled from the other by an electrostatic force of 1.0 N when the spheres are 2.0 m apart, what is the charge, in micro-coulomb, on the sphere with the smaller charge?

Answer 1

Explanation:

It is given that,

Let q₁ and q₂ are two small positively charged spheres such that,

$q_1+q_2=5\times 10^{-5}\ C$.............(1)

Force of repulsion between the spheres, F = 1 N

Distance between spheres, d = 2 m

We need to find the charge on the sphere with the smaller charge. The force is given by :

$F=k\dfrac{q_1q_2}{d^2}$

$q_1q_2=\dfrac{F.d^2}{k}$

$q_1q_2=\dfrac{1\ N\times (2\ m)^2}{9\times 10^9}$

$q_1q_2=4.45\times 10^{-10}\ C$............(2)

On solving the system of equation (1) and (2) using graph we get,

$q_1=0.0000384\ C=38.4\ \mu C$

$q_2=0.0000116\ C=11.6\ \mu C$

So, the charge on the smaller sphere is 11.6 micro coulombs. Hence, this is the required solution.