Two charges of equal magnitude, q and-q are fixed in place as shown.Another posi

Question

Two charges of equal magnitude, q and-q are fixed in place as shown.Another positive charge Q is at coordinate x located on the x-axis 1. a) What is the electrostatic potential at Q due to the charges q and-qin terms of a, q, and x? Find the electric field component E, due to charges q and -q along the x-axis at Q, in terms of o, a and x b) c) What is the net force acting on charge Q along the x axis, F, in terms of a, q, Q and x? d) what is the electrostatic potential energy of the system in terms of a, and x?

Explanation / Answer

Electrostatic potential at position of Q =

k* -q / x + k * q / (x-a)

= - k q/ x + kq /(x-a)

= kq [ 1/(x-a) - 1/x ]

= k q a / x(x-a)

b)

Ex = - k q / x^2 + k q / (x-a)^2

= kq [ (1/(x-a)^2 - 1/ x^2 ]

= kq [ (2xa - a^2) / x^2. (x-a)^2 ]

= kq a [ (2x-a) / {x(x-a)}^2 ] along positive x- axis

c)

Force is E * Q

Fx = kq a [ (2x-a) / {x(x-a)}^2 ] * Q

= kqQ a [ (2x-a) / {x(x-a)}^2 ]

d)

Electric potential energy of the system of 3 point charges =

k [ (q * -q / a) + ( q * Q / (x-a) ) + ( -q * Q /x ) ]

= kq [ Q / (x-a) - Q/x - q/a ]

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