Answer to Question #153228 in Electricity and Magnetism for zaina

Question

In 1955, a water bore that was 2231 m deep was drilled in Montana. Consider two

charges, q2 = 5.60 mC and q1, separated by a distance equal to the depth of the well. If

a third charge, q3 = 1.998 C, is placed 888 m from q2 and is between q2 and q1, this

third charge will be in equilibrium. What is the value of q1?

Answer 1

Answer

When three charges are in equilibrium then total electric forces are zero or also called both forces must be equal.

So can be written as

$\frac{kq_1q_3}{r^2}=\frac{kq_2q_3}{r'^2}$

$$\frac{q_1}{(2231-888)^2}=\frac{5.60\times10^{-3}}{(888)^2}$$

$q_1=\frac{1343\times1343\times5.60\times10^{-3}}{888\times888}$

So

Charge become

$q_1=12.81mC$