Question

Three identical point charges each of charge q are located at the vertices of an equilateral triangle as in the figure shown below. The distance from the center of the triangle to each vertex is a. (a) Show that the electric field at the center of the triangle is zero. (Submit a file with a maximum size of 1 MB.) This answer has not been graded yet. (b) Find a symbolic expression for the electric potential at the center of the triangle. (Use any variable or symbol stated above along with the following as necessary: ke for the Coulomb's constant.) V = (c) Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center.

Answer 1

Electric Field is a vector quantity. As the three charges are identical the magnitude of electric field produced by them at the centre of the triangle is constant and is always pointed either towards the verices or away from them. In both the cases if we resolve the x and y components of the electric fields we will get the resultants electric fields in x and y directions as zero. Therefore we can conclude that the electric field at the centre of the traingle is zero. But the electric potential is the potential energy per unit charge and it is a scalar quantity. Electric potential is the energy required to bring an unit charge from infinity to the specified point. As the electric potential is a scalar quantity and charges are identical the resultant electrical potential at the centre of the triangle is given as v1+v2+v3=3kq/r