Question

A collection of six positive point charges +q are situated at six corners of a regular heptagon centered on the origin, as shown below. The distance from the origin to each apex is a. Calculate the magnitude and direction of the electric field at the origin in terms of q, a, and physical constants.

A) E = 6kq/a^2, directed outward from the origin.
B) E = 6kq/a^2, directed inward toward the origin.
C) E = kq/a^2, directed outward from the origin.
D) E = kq/a^2, directed inward toward the origin.

Answer 1

The magnitude and direction of the electric field at the origin, due to the collection of six positive point charges +q situated at the corners of a regular heptagon centered on the origin, is given by E = 6kq/a², directed outward from the origin. Therefore, the correct answer is (A). (Option A)

Step-by-step explanation:

To calculate the electric field at the origin, we can use the principle of superposition. The electric field at a point due to multiple point charges is the vector sum of the electric fields produced by each individual charge. For a positive point charge +q, the electric field (E) at a distance r is given by Coulomb's law: E = kq/r², where k is Coulomb's constant.

Considering a regular heptagon with six charges, each situated at a corner of the heptagon centered on the origin, the distance from the origin to each charge is a. Due to the symmetry of the problem, the magnitudes of the electric fields produced by the charges at the same radial distance cancel each other out, except for one charge. Thus, the net electric field at the origin is the sum of the individual electric fields, resulting in E = 6kq/a².

The direction of the electric field is outward because the positive charges produce electric fields that radiate away from them. Therefore, the correct answer is (A) E = 6kq/a², directed outward from the origin.(Option A)