Question

Two charges, 12 mC and 11 mC, are fixed in place 1.0 m apart, with the second one to the right. Find the magnitude and direction of the net force on a -2.0 nC charge, placed at the following locations:

a) halfway between the two: |F|=

b) b) half a meter to the left of the 12 mC charge: |F|=

Answer 1

Given the charge q1 = 12mC = 12 x 10-3C and q2 = 11mC = 11 x 10-3C. The charge q2 is d = 1m from q1. Thethird charge q3 = -2nC = -2 x 10-9C.

a) When q3 is placed halfway between q1 and q2, the charge q3 is at a distance of r = 0.5m from both q1 and q2. The force acting on q3 due to q1 is given by,

Since q1 is positive and q3 is negative, q1 attracts q3 towards q1. So the direction of F(3,1) is towards left.

The force acting on q3 due to q2 is given by,

Since q2 is positive and q3 is negative, q2 attracts q3 towards q2. So the direction of F(3,2) is towards right.

The net force acting on q3 in this case is,

So the net force on q3 is 0.072N and the direction of this net force is towards left.

b) When q3 is placed half a meter to the left of the 12 mC charge, it is 1.5m from the 11mC charge. The force acting on q3 due to q1 is,

Since q1 is positive and q3 is negative, q1 attracts q3 towards q1. So the direction of F(3,1) is towards right.

The force acting on q3 due to q2 is given by,

Since q2 is positive and q3 is negative, q2 attracts q3 towards q2. So the direction of F(3,2) is towards right.

The net force acting on q3 in this case is,

So the net force on q3 is 0.952N and the direction of this net force is towards right.