Background Info: A square with two equal negatively charged point objects in opp

Question

Background Info: A square with two equal negatively charged point objects in opposite corners and a positively charged point object of 1/3 the magnitude of the negative charges in a third corner. You will calculate the electric potential at the remaining corner of the square.

A) Write down equations for the (scalar) electric potentials at the point of interest caused by each of the three charged objects using the value of each charge and the size of the square.

B)Determine the total electric potential at the point of interest by adding the electric potentials from each point charge. Remember that the charges are of different sign.

Explanation / Answer

A)
Let size of square be a
q1 = -q
r1 = a
V1 = k*q1/r1 = k*(-q)/a = -k*q/a

q2=-q
r2=a
V2 = k*q2/r2 = k*(-q)/a = -k*q/a

q3 = q/3
r2 = a*sqrt(2)
V3 = k*q3/r3 = k*(q)/3*sqrt(2)*a = k*q/3*sqrt(2)*a

b)
V = V1 + V2 + V3
    = - k*q/a -k*q/a + k*q/3*sqrt(2)*a
    = -2*k*q/a + 0.236* k*q/a
   = -1.764*k*q/a

Here k = 9*10^9

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