Question

Two positively charged spheres of mass 1 kg each are held in free space, 1 meter away from each other. The two spheres have a charge of 1.0541 × 10?5C each. One charge is released while the other is still held fixed.

a) Find the speed of the moving charge when it is 2 meters away from the fixed charge.

b) Find the speed of the moving charge when it is 3 meters away from the fixed charge.

K = 9 × 109Nm2/C 2

Answer 1

let

m = 1 kg
q1 = q2 = 1.0541*10^-5 C

a) r1 = 1 m, r2 = 2 m

Apply conservation of energy

initial mechanical energy = final mechanical energy

k*q1*q2/r1 = k*q1*q2/r2 + (1/2)*m*v^2

9*10^9*(1.0541*10^-5)^2/1 = 9*10^9*(1.0541*10^-5)^2/2 + (1/2)*1*v^2

==> v = 1.000 m/s

b) r1 = 1 m, r2 = 3 m

Apply conservation of energy

initial mechanical energy = final mechanical energy

k*q1*q2/r1 = k*q1*q2/r2 + (1/2)*m*v^2

9*10^9*(1.0541*10^-5)^2/1 = 9*10^9*(1.0541*10^-5)^2/3 + (1/2)*1*v^2

==> v = 1.154 m/s