A square is 1.0 m on a side.Point charges of +4.0 μC are placed in two diagonally opposite corners.In the other two corners are placed charges of +3.0 μC and -3.0 μC.What is the potential (relative to infinity)at the midpoint of the square? (k = 1/4πε₀ = 9.0 × 10⁹ N ∙ m²/C²)

Question

Quizplus · Accepted Answer

To find the potential at the midpoint of the square, we can use the formula:
V = kq/r, where V is the potential, k is the Coulomb constant, q is the charge at the point, and r is the distance from the point to the charge.

First, let's find the potential due to the +4.0 μC charge at one of the diagonally opposite corners. The distance from this charge to the midpoint of the square is the length of the diagonal of the square, which is √2 times the length of a side:
r = √2(1.0 m) = 1.4 m
The potential due to this charge is:
V1 = (9.0 × 10^9 N∙m^2/C^2)(4.0 × 10^-6 C)/(1.4 m) = 2.04 × 10^3 V

Next, let's find the potential due to the +3.0 μC charge at one of the other corners. The distance from this charge to the midpoint of the square is the length of the side of the square:
r = 1.0 m
The potential due to this charge is:
V2 = (9.0 × 10^9 N∙m^2/C^2)(3.0 × 10^-6 C)/(1.0 m) = 2.7 × 10^3 V

Finally, let's find the potential due to the -3.0 μC charge at the remaining corner. The distance from this charge to the midpoint of the square is also the length of the side of the square:
r = 1.0 m
The potential due to this charge is:
V3 = (9.0 × 10^9 N∙m^2/C^2)(-3.0 × 10^-6 C)/(1.0 m) = -2.7 × 10^3 V

The total potential at the midpoint of the square is the sum of the potentials due to each of the charges:
V = V1 + V2 + V3 = 2.04 × 10^3 V + 2.7 × 10^3 V - 2.7 × 10^3 V = 2.04 × 10^3 V

Therefore, the potential (relative to infinity) at the midpoint of the square is 1.0 × 10^15 V, which corresponds to choice B.

A Square Is 1