Charges of and are fixed at the vertices and of an equilateral triangle of side

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Charges of

+5.0\,\mu\text{C}

and

-3.0\,\mu\text{C}

are fixed at the vertices

A

and

B

of an equilateral triangle

ABC

of side

0.20\,\text{m}

. What charge should be placed at the third vertex

C

so that the electric potential at the centroid of the triangle becomes zero? Use

\dfrac{1}{4\pi\varepsilon_{0}} = 9\times10^{9}\,\text{N m}^2\text{C}^{-2}

. (i) Calculate the distance from any vertex of an equilateral triangle to its centroid. (ii) Write an expression for the total electric potential at the centroid due to the three charges, taking the charge at

C

to be

q

. (iii) Hence determine the magnitude and sign of the charge required at

C

so that the potential at the centroid is zero.

Related theory

Electric Potential
Potential due to a system of charges
Electrostatic Potential and Capacitance

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