Question

Three point charges have the following values: Q1 = +4.0nC, Q2 = −5.0nC, and Q3 = −8.0nC. The charges are placed at the vertices of a rectangle that has a height of h = 60 cm and a width of w = 80 cm (and the fourth vertex of this rectangle remains empty). Q1​ is placed at the top-left vertex; Q2​ is placed at the top-right vertex; and Q3 is placed at the bottom left vertex. What is the electric potential at the empty bottom right vertex? (Take the electric potential to be zero when you are infinitely far away from all of the charges.)

Answer 1

To find the electric potential at the empty bottom right vertex, we need to calculate the electric potential contribution from each of the three charges and sum them up. Using the equation V = kQ/r, where V is the electric potential, k is the electrostatic constant, Q is the magnitude of the charge, and r is the distance from the charge to the point, we can calculate the electric potentials due to each charge and add them together. The total electric potential at the bottom right vertex is 188.25 x 10^9 V.

Step-by-step explanation:

To find the electric potential at the empty bottom right vertex, we need to calculate the electric potential contribution from each of the three charges. The electric potential at a point due to a charge is given by the equation: V = kQ/r, where V is the electric potential, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance from the charge to the point. We can calculate the electric potential at the empty bottom right vertex by summing up the electric potential due to each charge and taking into account the distance between the charges and the vertex.

First, let's calculate the electric potential due to Q1. The distance between Q1 and the vertex is the height of the rectangle, h. Plugging in the values, we get V1 = (9 x 10^9 Nm^2/C^2)(4.0 x 10^-9 C)/(0.6 m) = 60 x 10^9 V.

Next, let's calculate the electric potential due to Q2. The distance between Q2 and the vertex is the width of the rectangle, w. Plugging in the values, we get V2 = (9 x 10^9 Nm^2/C^2)(5.0 x 10^-9 C)/(0.8 m) = 56.25 x 10^9 V.

Finally, let's calculate the electric potential due to Q3. The distance between Q3 and the vertex is the diagonal of the rectangle, d. Using the Pythagorean theorem, we can calculate the diagonal as d = sqrt(h^2 + w^2) = sqrt((0.6 m)^2 + (0.8 m)^2) = 1 m. Plugging in the values, we get V3 = (9 x 10^9 Nm^2/C^2)(8.0 x 10^-9 C)/(1 m) = 72 x 10^9 V.

Now, we can find the total electric potential at the bottom right vertex by summing up the contributions from each charge: Vtotal = V1 + V2 + V3 = 60 x 10^9 V + 56.25 x 10^9 V + 72 x 10^9 V = 188.25 x 10^9 V.