Question

24 point charges of +2.4 micro-coulombs are placed on the perimeter of a circle with a radius of 1.3 meters. Also, charges of -2 micro-coulombs, -6 micro-coulombs, and -4 micro-coulombs are also placed on this perimeter as well. Another charge of +6 micro-coulombs with a mass of 0.16 kg is originally moving at 3.2 m/s at the center of the circle. How fast is this charge moving in m/s when it is very, very, far away from the other charges?

Answer 1

Net charge at perimeter = 24*2.4 - 2 - 6 - 4 = 45.6 micro-C
Potential at the center = kQ/r = 9x10⁹ * 45.6*10^-6 / 1.3
                                               = 315692 V
Potential at infinity ( very, very far away from charges) = 0
Total mechanical energy of moving charge is conserved
Initial potential energy = qV = 6x10^-6*315692 = 1.9 J
Final potential energy = qV = 6*0 = 0
Initial kinetic energy = mV_i² /2 = 0.16 *3.2²/2 = 0.82 J
Final kinetic energy = mV_f²/2 = 0.08 V_f²
1.9 + 0.82 = 0 + 0.08V_f²
Vf = 5.83 m/s