Three identical point charges each of charge q are located at the vertices of an

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.)

(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.

Explanation / Answer

a)

x component of Electric field at centre

= k q cos(30)/ a^2 - k q cos(30) / a^2 + 0

= 0

y component of electric field at centre

= k q sin(30) / a^2 + k q sin(30) / a^2 - k q / a^2

  = 2 k q sin(30) /a^2 - k q / a^2

= k q / a^2 - k q / a^2 = 0

Hence Electric field at the centre is zero

b) Eelctric potenial at centre = ke q / a + ke q / a + ke q / a

V = 3 ke q / a

c) Electric potential is a scalar quantity , you have to just add the values to get the net value . But Electric field is a vector quantity, you have to consider directions to get the net values. Here centre is equidistant from all charges and net electric field is zero when directions are considered. Hence electric potential is not zero, yet the electric field is zero at the center

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