Answer to Question #212248 in Physics for Envy

Question

Two charges, q1 and, q2, are located at the origin and at (0.50 m, 0), respectively. Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if

(a) q 1 and q2 are like charges of equal magnitude.

(b) q1 and q2 are unlike charges of equal magnitude.

(c) q1=+3.0 μC and q2=−7.0 μC?

Answer 1

a)

$$x=0.25\ m$$

b) Nowhere. It is not possible because one charge will always attract and the other repel q₃ unequally.

c)

$$\frac{3}{x^2}=\frac{7}{(x+0.5)^2}\\x=-0.95\ m\\y=0\ m$$