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Using point charges to determine potential at a given point

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3 point charges Q1, Q2, Q3 are located in the xy plane at points (-10,0), (10,0) and
(-5,12) respectively.

The charges are given values Q1 = 5 uC, Q2 = -10 uC, Q3 = 8 uC. You may assume that the distance between charges is in units of cm

(A) Calculate the Electric Potential at the origin, point (0,0)

(B) Determine the work done in moving a charge of 3 uC to the origin from infinity under this potential

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Solution Summary

This solution goes through a typical exam question and asks to consider a system of 3 point charges of known values located at set points in the xy plane. It asks then to determine the electric potential at another given point (the origin) due to these three charges. The mathematics is explained and the step by step approach to solving the problem is developed using linear algebra.

The second part of the problem then asks to determine the work done in bringing a known charge from infinity to the original point in question.

Solution Preview

First draw a diagram of the situation (SEE ATTACHMENT)

PART A: Solution.

Electric potential (V) at a point can be given as

V = k*q/r (1)

where k = 1/4pi*epsilon (epsilon = epsilon0 the permittivity of free space if the medium separating the charges is air or vacuum)

and where r is the distance of separation between the point of interest and the charges, q is the charge at a distance r.

Therefore the potential at the origin V(0,0) can be derived as

V(0,0)=Potential due to Q1(V1) + Potential due to Q2(V2) +Potential due to Q3(V3) (2)

Now we calculate each of these individual contributing ...

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