Question

two point charges with charge q are initially separated by a distance d. if you double the charge on both charges, how far should the charges be separated for the potential energy between them to remain the same

Answer 1

r ’= 4 r

Step-by-step explanation:

Electric potential energy is

U =
`k (q_1q_2)/(r_(12))`k q1q2 / r12

in this exercise

q₁ = q₂ = q

U = k q² / r

for when the charge change

U ’= k q’² / r’

indicate that

q ’= 2q

U ’= U

we substitute

U = k (2q) ² / r ’

U = 4 k q² / r ’

we substitute

`k \ (q^2)/(r) = 4 k \ (q^2)/(r')`k q² / r = 4 k q² / r ’

r ’= 4 r