Question

Two tiny particles having charges of +5.00 μC and +7.00 μC are placed along the x-axis. The +5.00-µC particle is at x = 0.00 cm, and the other particle is at x = 100.00 cm. Where on the x-axis must a third charged particle be placed so that it does not experience any net electrostatic force due to the other two particles?

4.58 cm

45.8 cm

50 cm

9.12 cm

91.2 cm

Answer 1

The formula for electric field due to point charge is

E = kq/r^2

let consider third charge is at x distante from the origin then from the equlibrium condition

k Q1 / x1^2 - k Q2 / x2^2 = 0

x1 + x2 = 100cm = 1m

5 / x^2 = 7 / (1-x)^2

(1-x)/x = sqrt(7/5) = 1.1832

1-x = 1.1832 x

1= 2.1832 x

x = 1/2.1832

=45.8 cm