The identical point barges each of charge g are located at the vertices of an eq

Question

The identical point barges each of charge g 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 held at the center of the triangle is zero. (Submit a fee 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: k_e for the Constant.) (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)
let q1 = q2 = q3 = q

electric field produced by each charge, E1 = E2 = E3 = E = k*q/a^2

here the angle between E1 and E2 is 120 degrees

so, E12 = sqrt(E1^2 + E2^2 + 2*E1*E2*cos(120))

= E

here the resultant E1 and E2 is E and it is opposite to E3

so, Enet = E12 - E3

= E - E

= 0

b) V = V1 + V2 + V3

= k*q/a^2 + K*q/a^2 + k*q/a^2

= 3*k*q/a^2

c) In order to bring a test charge from infinite to the center of triangle we need to do work, the work is stored as potential energy.

so, potential is not at the center.

Vnet = W/Q (workdone per unit charge)

here W is not zero so, Vnet is zero)

But we when we place the test charge at the center net force acting in it zero.

so, Enet = Fnet/Q (Force per unit charge)

= 0/Q

= 0

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