Calculate the magnitude and direction of the Coulomb force on each of the three charges connected in series:

Question

1st - 6 micro Coulombs (positive charge)
2nd - 1.5 micro Coulombs (positive charge)
3dr - 2 micro Coulombs (negative charge)
Distance between 1st and 2nd - 3cm
Distance between 2nd and 3rd - 2cm

Answer 1

We'll first calculate the Coulomb force between 1st and 2nd charges, then between 2nd and 3rd charges.

Coulomb's law states that the force between two charges is given by:

F = k * q1 * q2 / r^2

where F is the force, k is the Coulomb constant (approx. 8.99 * 10^9 N m^2 C^-2), q1 and q2 are the charges, and r is the distance between the charges.

Force between 1st and 2nd charges:
q1 = 6 * 10^-6 C (micro = 10^-6)
q2 = 1.5 * 10^-6 C
r = 3 * 10^-2 m (cm = 10^-2)
F12 = k * q1 * q2 / r^2
F12 = (8.99 * 10^9 N m^2 C^-2) * (6 * 10^-6 C) * (1.5 * 10^-6 C) / (3 * 10^-2 m)^2
F12 ≈ 1.346 N (attractive force, since both charges are positive)

Force between 2nd and 3rd charges:
q1 = 1.5 * 10^-6 C
q2 = -2 * 10^-6 C (negative charge)
r = 2 * 10^-2 m
F23 = k * q1 * q2 / r^2
F23 = (8.99 * 10^9 N m^2 C^-2) * (1.5 * 10^-6 C) * (-2 * 10^-6 C) / (2 * 10^-2 m)^2
F23 ≈ -1.798 N (attractive force, since one charge is positive and the other is negative)

To find the net force on the 2nd charge, we'll use vector addition since the forces act in opposite directions.

F_net = F12 + F23
F_net = 1.346 N + (-1.798 N)
F_net = -0.452 N

The net force on the 2nd charge is 0.452 N in the direction towards the 3rd charge (since it's negative).

The force on the 1st and 3rd charges will be equal in magnitude but opposite in direction to the forces we calculated for the 2nd charge. The 1st charge will experience an attractive force of 1.346 N towards the 2nd charge, while the 3rd charge will experience an attractive force of 1.798 N towards the 2nd charge.