Question

Two small nonconducting spheres have a total charge of (a) When placed 28.0 cm apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each

Answer 1

q = 1 x 10⁻⁵ C = 10 μC

Step-by-step explanation:

The repulsive force between the charges is given by Coulumb's Law:

`F = (kq_(1)q_(2))/(r^(2))\\`

where,

F = Electrostatic Force = 12 N

k = Coulomb's Constat = 9 x 10⁹ Nm²/C²

r = distance between charges = 28 cm = 0.28 m

Since the values or charges are not given. We assume that both charges have same mahnitude. Therefore,

q₁ = q₂ = q = charge on each sphere = ?

Therefore,

`12\ N = ((9\ x\ 10^(9)\ Nm^(2)/C^(2))q^(2))/((0.28\ m)^(2)) \\\\q^(2) = ((12\ N)(0.28\ m)^(2))/(9\ x\ 10^(9)\ Nm^(2)/C^(2))\\q = \sqrt{1\ x\ 10^(-10)\ C^(2)}\\`

q = 1 x 10⁻⁵ C = 10 μC