Three charges each of value q are placed at the corners of an equilateral triangle. A fourth charge Q is placed at the center of the triangle.
a. Find the net force on charge q.
b. If `Q = -q`, will the charges at the corners move toward the center or fly away from it ?
c. For what value of Q at O will the charges remain stationary ?
d. In situation (c), how much work is done in removing the charges to infinity?

Options

A. `(-q)/(sqrt(3))`
B. `-sqrt(3)q`
C. `sqrt(3)q`
D. `(q)/(sqrt(3))`

Answer

A

Explanation

Net force on q is zero
Let the side of equilateral triangle be equal to a
`implies 2 q^2/(4 pi e_0 a^2) cos 30^@+ (Q q)/(4 pi e_0(a//sqrt3)^2)=0`
`implies Q=-2/3 q.sqrt3/2 implies Q=-q//sqrt3`