How to find potential from 2 charges through 4 points?

Could someone help with this assignment please?

The figure shows two positive charges, Q and 2Q. They are creating an electric potential through the points of A, B, C and D. Write down the following; Which point has the highest, second highest, second lowest and lowest potential.

enter image source here

1 Answer
May 9, 2018

#V_D > V_C>V_B>V_A#


Since the potential caused by a positive charge falls off with the distance, this problem can be worked out without any explicit calculation.

  • Point D has the highest potential, being closest to both the charges
  • point C comes next
  • among A and B, B has the higher potential, since it is closer to the bigger charge than A

To verify, here are the actual values

  • #V_D= 1/(4pi epsilon_0)(Q/(d/2)+(2Q)/(d/2))=1/(4pi epsilon_0)(6Q)/d#
  • #V_C= 1/(4pi epsilon_0)(Q/(d/sqrt2)+(2Q)/(d/sqrt2))=1/(4pi epsilon_0)(3sqrt2 Q)/d#
  • #V_B= 1/(4pi epsilon_0)(Q/(sqrt2 d)+(2Q)/(d))=1/(4pi epsilon_0)((4+sqrt2) Q)/(2d)#
  • #V_B= 1/(4pi epsilon_0)(Q/( d)+(2Q)/(sqrt2 d))=1/(4pi epsilon_0)((1+sqrt2) Q)/(d)#