A positive point charge + Q is located on the x axis at x = - a . (a) How much w

Question

A positive point charge +Q is located on the x axis at x = -a.

(a) How much work is required to bring an identical point charge from infinity to the point on the x axis at x = +a? (Use any variable or symbol stated above along with the following as necessary: k for the Coulomb's constant.)
W =

(b) With the two identical point charges in place at x = -a and x = +a, how much work is required to bring a third charge -Q from infinity to the origin? (Use any variable or symbol stated above along with the following as necessary: k for the Coulomb's constant.)
W =

(c) How much work is required to move the charge -Q from the origin to the point on the x axis at x = 2a along the semicircular path shown? (Use any variable or symbol stated above along with the following as necessary: k for the Coulomb's constant.)
W =

Explanation / Answer

(A) at inifinity, potential = 0

at x = a, Potential = k Q / (a- (-a))

PE = k Q/ 2a

Work done = Q delta(PE) = k Q^2 / 2 a

(B) potential at origin = kQ/a + kQ/a = 2 k Q/a

Work done = - Q (2 k Q /a - 0 )

= - 2 k Q^2 / a

(C) potential at x = 2 a

V = k Q /a + kQ/(3a) = 4 k Q / 3 a

W = - Q (4 k Q / 3a - 2 k Q / a)

= 2 k Q ^2 / 3 a^2

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