Question

6. Three point charges are arranged along the x-axis. Charge q1 = -2 uC is at x=0.5 m, and charge q2= 5 uC is at x=-0.5m. At what position(s) can the third charge q3=1 uC be located if we want the net force on q3 to be zero

Answer 1

Electrostatic force is given by:

F = k*Q1*Q2/R^2

Where force will be attractive if both charge have opposite signs and force will be repulsive if both charges have same sign

Now net force on charge q3 is given that zero and q3 (positive charge) should be located on x-axis.

So q3 charge should be located towards the right side of q1 at 'd' distance, So that net force on it can be zero. (since q1 < q2)

Fnet = F1 - F2 = 0

F1 = Force on q3 due to q1

F2 = Force on q3 due to q2

F1 = F2

k*q3*q1/r1^2 = k*q3*q2/r2^2

q1/q2 = (r1/r2)^2

q1 = -2*10^-6 C & q2 = 5*10^-6 C

r1 = distance b/w q1 and q3 = d

r2 = distance b/w q2 and q3 = d + 0.5 + 0.5 = d + 1

2*10^-6/(5*10^-6) = [d/(d + 1)]^2

(d + 1)/d = sqrt 2.5 = 1.58

d + 1 = 1.58*d

d = 1/0.58

d = 1.724 m

x = d + 0.5 = 1.724 + 0.5 = 2.224 m

So third charge should be located at x = 2.224 m, (toward the right of origin)

Let me know if you've any query.