Question

# Four charges (-e,e,-e,e) in a row are separated from their neighboring charges by 3×10^(-10)m. Calculate the...

Four charges (-e,e,-e,e) in a row are separated from their neighboring charges by 3×10^(-10)m. Calculate the work required to remove the positive charge on the right side to infinity.

let d = 3*10^-10 m
q1 = -e
q2 = +e
q3 = -e
q4 = +e
potential at the location of right side charge,

Vi = k*q1/(3*d) + k*q2/(2*d) + k*q3/d

= k*(-e)/(3*d) + k*e/(2*d) + k*(-e)/d

= -(5/6)*k*e/d

potential at infinite distance, Vf = 0

Workdone in moving the charge q4 to infinity, W = q4*(Vf - Vi)

= e*(0 - (-(5/6)*k*e/d ) )

= (5/6)*k*e^2/d

= (5/6)*9*10^9*(1.6*10^-19)^2/(3*10^-10)

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