Question

A 4.0 µC point charge and a 3.0 µC point charge are a distance L apart. Where should a third point charge be placed so that the electric force on that third charge is zero? (Use the following as necessary: L.)

Answer 1

Answer:

Q must be placed at 0.53 L

Explanation:

Given  data:

q_1 = 4.0 μC , q_2 = 3.0μC

Distance between charge is L

third charge q be placed at  distance x cm from q1

The force by charge q_1 due to q is

$F1 = \frac{k q q_1}{x^2}$

$F1 = \frac{k q ( 4.0 μC )}{ x^2}$                  ----1

The force by charge q_2 due to q is

$F2 = \frac{k q q_2}{(L-x)^2}$

$F2 = \frac{kq (3.0 μC)}{(L-x)^2}$                   --2

we know that net electric force is equal to zero

F_1 = F_2

$\frac{k q ( 4.0 μC )}{x^2} =\frac{k q ( 3.0 μC )}{(l-x)^2}$

$\frac{4}{3}*(L-x)^2 = x^2$

$x = \sqrt{\frac{4}{3}*(L - x)$

$L-x = \frac{x}{1.15}$

$L = x + \frac{x}{1.15} = 1.86 x$

x = 0.53 L

Q must be placed at 0.53 L