Question

A charge 4q is at the origin, and a charge of -3q is on the positive x-axis at x = a. Where would you place a third charge so it would experience zero net electric force? (Note: Either enter your answer as an unevaluated expression, e.g., (3/2 + sqrt(3))a, or if evaluated, use 2 decimal places.) Your expression should be in terms of the given variable.

Answer 1

6.45 a

Step-by-step explanation:

Charge on O, q1 = 4q

Charge on A, q2 = - 3 q

OA = a

Let the net force is zero at point P, where AP = x , let a charge Q is placed at P.

The force on point P due to the charge q1 = The force on point P due to the

charge q2

By using Coulomb's law

`(Kq_(1)Q)/(OP^(2))=(Kq_(2)Q)/(AP^(2))`

`\frac {K4qQ}{(a+x)^(2)}= \frac {K3qQ}{x^(2)}`

`(a+x)/(x)=\sqrt{(4)/(3)}`

`(a+x)/(x)=1.155`

a + x = 1.155 x

0.155 x = a

x = 6.45 a

Thus, the force is zero at x = 6.45 a.