A particle, having a charge +5 μC, is initially at rest at the point x = 30 cm on the x-axis. The particle begins to move due to the presence of a charge Q that is kept fixed at the origin. Find the kinetic energy of the particle at the instant it has moved 15 cm from its initial position if (a) Q =+15μC and (b) Q = -15μC.

Given

Charge Q=+15 μC

Charge q =+ 5 μC

The distance between resting position of charge q and Q=30 cm

Displacement of charge q due to charge Q= 15 cm

Formula used:

The kinetic energy= change in potential energy =U_F-U_i

U_f is final potential energy, U_i is initial potential energy

Potential energy

Where,

K is the constant its value=9 × 10⁹ Nm²/c²

Q ,q are the charges

R is the distance between the charges

(a) Finding the initial potential energy when q is at res

Putting the values of Q=15 μC ,q=5 μC and r=30 cm in the equation(2), we get

Putting the value of Q=15 μC, q=5 μC and r=45 cm in the equation(2), we get final potential energy

The kinetic energy = U_i - U_f = 2.25 – 1.5 =0.75 J

(b) Finding the initial potential energy when q is at res

Putting the values of Q=15 μC ,q=5 μC and r=30 cm in the equation(2), we get

Putting the value of Q=15 μC, q=5 μC and r=45 cm in the equation (2), we get final potential energy

The kinetic energy = U_i - U_f = -2.25 – (-4.5) =2.25 J

Conclusion:

The final kinetic energy of the charge q(5 μC) when Q is 15 μC is 0.75 J.

The final kinetic energy of the charge q(5 μC) when Q is -15 μC is 2.25 J