Question

Two charges q1 = 5 µC, q2 = -30 µC, are L = 17 cm apart. A third charge is to be placed on the line between the two charges. How far from q1 should the third charge beplaced so that the net electric force on the third charge is minimized?

Answer 1

Given that Two charges q1 = 5 µC, q2 = -30 µC,
distance between the charges is L=0.17m
let r is the distance of the third charge from the first charge
then the electrostatic force on the charge is
kq1q3/r²

the electrostatic force due to the second charge is
kq2q3/(L-r)² therefore

q2/(L-r)² = q1/r²


30/(0.17-r)² = 5/r²

6/(0.17-r)² = 1/r²
r=0.17-r/√6
3.449r=0.17
r=0.049m
that is the third charge has to keep at a distance 4.9cm from the first charge