Two small spheres are located 0.50 m apart. Both have the same...

Question

Two small spheres are located 0.50 m apart. Both have the same charge on them. If the repulsive force is 5.0 N, what charge is on the spheres, in μC?

Answer 1

The electrostatic force between two charges is given by

F_e = (kq₁q₂) / r²
 
Given
F_e = 5 N

r = 0.5 m
q₁ = q₂ = q
k = 9 × 10⁹ N * m²/C²

 

Substitute

 

F_e = kq²/r²        q = √ (F_er²/k)

 

If you substitute in the above equation, your answer will be in Coulombs.

You will need to divide by a further 10^-6 to convert to µC.

Answer 2

Use the formula for electrostatic force.

 

F_e = (kq₁q₂) / r²

 

where:

F_e = 5 N

q₁ = q₂

k = 9 × 10⁹     N * m²/C²

 

 

5 = kq / (0.5)²

 

 

Solve for q.  Since the force is repulsive, the charges have the same polarity.  They are either both negative or both positive, depending on the value of q you solved for.