Question

A square in the x-y plane in free space has a point charge of +Q at corner (a/2, a/2), the same at corner (a/2, -a/2), and a point charge of -Q at each of the other two corners.

(a) Find the electric potential at any point P along the x axis.
(b) Evaluate Vtx = a/2.

Answer 1

The question is on calculating the electric potential at a point P along the x-axis due to four point charges at the corners of a square on the x-y plane in free space. By using the formula V = kQ/r and the principle of superposition, we can sum the potentials from each charge to find the total potential at P.

Step-by-step explanation:

The question deals with finding the electric potential at a point P on the x-axis created by point charges located at the corners of a square on the x-y plane. Since the potential due to a point charge is given by V = kQ/r (where k is Coulomb's constant, Q is the charge, and r is the distance to the point of interest), we can find the potential at P by summing the potentials due to each of the four charges and taking into account their signs and distances from point P.

(a) To find the electric potential at point P, we use the principle of superposition, which states that the total potential at a point due to several charges is the algebraic sum of the potentials due to each charge separately. Thus, V = V1 + V2 + V3 + V4, where V1 and V2 are the potentials due to the positive charges and V3 and V4 are the potentials due to the negative charges, each calculated using the formula V = kQ/r.

(b) At point P (x = a/2), we can find the distances to each charge by geometry and calculate the potential at this specific point following the superposition principle.