Question

Point charges of 5.00 µC and –3.00 µC are placed 0.250 m apart.
(a) Where can a third charge be placed so that the net force on it is zero?
(b) What if both charges are positive?

Answer 1

here,

q1 = 5 uC , q2 = - 3 uC

r = 0.25 m

a)

let the third charge be placed x m from the 3 uC charge

the net force on third charge

F = k * q1 * q /(x + r)^2 - k * q2 * q /( x)^2

as the net force is zero

0 = k * q1 * q /(x + r)^2 - k * q2 * q /( x)^2

0 = q1 /(x + 0.25 )^2 - q2 /( x )^2

0 = 5/(x + 0.25)^2 - 3 /(x)^2

solving for x

x = 0.85 m

the third charge must be placed 0.85 from q2

b)

when both the charges are positive

the third charge must be placed between them

let the third charge be placed x m from the 3 uC charge

the net force on third charge

F = k * q1 * q / (r - x)^2 - k * q2 * q /( x)^2

as the net force is zero

0 = k * q1 * q / (r - x)^2 - k * q2 * q /( x)^2

0 = q1 /(0.25 - x )^2 - q2 /( x )^2

0 = 5/(0.25 - x)^2 - 3 /(x)^2

solving for x

x = 0.11 m