Two particles, with charges of q_1 = 80.0 nc and q_2 = 80.0 nc, are placed at th

Question

Two particles, with charges of q_1 = 80.0 nc and q_2 = 80.0 nc, are placed at the points with coordinates (0, 4.0 cm) and (0, -4.00 cm) as shown in the figure below. A particle with charge q_3 = 40.0 nC is located at the origin. Find the electric potential energy of the configuration of the three fixed charges. J A fourth particle, with a mass of 2.07 times 10^-13 kg and a charge of q_4 = 160.0 nC, is released from rest at the point (3.00 cm, 0). Find its speed after it has moved freely to a very large distance away. m/s

Explanation / Answer

Here, for the electric potential energy of the system

we will add potential energy due to all the pair of charges

U = 9 *10^9 * 10^-9 * 10^-9 * (80 *(-80)/0.08 - 80 * 40/0.04 + 40 * 80/0.04)

U = - 7.2 *10^-4 J

the potential energy of the system is -7.2 *10^-4 J

b)

let the speed of the forth charge is v

change in potential energy = 0.5 * m * v^2

as the potential due to q1 and q2 will be zero at the location of q4 as both are cancelled out.

9 *10^9 * 160 *10^-9 * 40 *10^-9/.03 = 0.5 * 2.07 *10^-13 * v^2

solving for v

v = 1.36 *10^5 m/s

the speed of the forth particle is 1.36 *10^5 m/s

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