Question

Given the diagram below with positive and negative charges separated by the distance d, how much work (in Joules) would the electric field created by the pictured charges do on a separate $+1.0C$ charge in moving it from point A to point B?
The blue charge is negative. The red charge is positive.
Answer are expressed in terms of k (the coulomb constant) and given distances

• A. $\frac{k}{2d}$
• B. $\frac{-k}{2d}$
• C. $\frac{k}{4d}$
• D. $\frac{-k}{4d}$
• E. $\frac{-k}{d}$

Answer 1

Answer: (D)

$\frac{-k}{4d}$

Electrostatic potential at point A due to charges $-1.0C$ and $+1C$ ,

$V_A=k(-1/4d+1/2d)=k/4d$ ,

Electrostatic potential at point B due to charges $-1.0C$ and $+1C$ ,

$V_B=k(-1/d+1/d)=0$ ,

therefore $V_B-V_A=0-k/4d$ ,

now we have , $W_{AB}=V_B-V_A/q$ ,

so $W_{AB}=-k/4d$ (q=+1.0C)