Question

Three particles with equal positive charges q are at the corners of an equilateral triangle of side a as shown in the figure below. (a) At what point, if any, in the plane of the particles is the electric potential zero? (b) What is the electric potential at the position of one of the particles due to the other two particles in the triangle? (Use any variable or symbol stated above along with the following as necessary: ke.)

Answer 1

Concepts and reason

The concepts used to solve this problem are electric potential and superposition Principle.

Initially, use the concept of electric potential to find the point in the plane of the particles where the electric potential is zero.

Finally, use the relation between electric potential, charge, and distance to find the electric potential at the position of one of the particles due to the other two particles in the triangle.

Fundamentals

The total potential at a point is the algebraic sum of the individual potential created by each charge.

Electric potential is a scalar quantity.

Expression for the electric potential due to a point charge is,

Here, the electric potential is , coulomb’s constant is , charge is , and the distance is .

“Principle of superposition states that the electric potential at a point due to the other charges will be equal to the sum of potential due to the each charge at the given point”.

(a)

Electric potential is a scalar quantity.

The total potential at a point is the algebraic sum of the individual potential created by each charge.

All the charges are equal and positive in charge and they create positive potentials.

Therefore, there is no neutral point for potential on the plane of the triangle.

(b)

Expression for the electric potential due to charge is,

Expression for the electric potential at the position of one of the particles due to the other two particles in the triangle is,

Here, charge of first particle is , charge of second particle is , distance from the first particle is , and distance from the second particle is .

Substitute for and and for and .

Here, the coulomb’s constant is equal to .

Therefore, the net electric potential at the position of one of the particles in the triangle is .

Ans: Part a

Thus, there is no neutral point for potential on the plane of the triangle.

Part b

Thus, the net electric potential at the position of one of the particles in the triangle is .