Question

Three +3.0-μC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a −3.0-μC charge. Find the magnitude of the electric field at the center of the square. (k=1/4πϵ0=8.99×109 N · m2/C2)

Answer 1

The magnitude of the electric field at the center of the square is 0 N/C.

Step-by-step explanation:

To find the magnitude of the electric field at the center of the square, we can calculate the electric field due to each point charge individually and then add them up. The electric field due to a point charge is given by the formula E = k * q / r^2, where k is the electrostatic constant (8.99×10^9 N · m^2/C^2), q is the charge, and r is the distance from the charge.

First, let's calculate the electric field due to each of the three +3.0 μC charges. The distance from each charge to the center of the square is 0.5 m, since the side of the square is 0.5 m.

E₁ = (8.99×10^9 N · m^2/C^2) * (3.0×10^(-6) C) / (0.5 m)^2 = 2.16×10^6 N/C

Next, let's calculate the electric field due to the -3.0 μC charge at the last corner of the square. The distance from this charge to the center of the square is also 0.5 m.

E₂ = (8.99×10^9 N · m^2/C^2) * (3.0×10^(-6) C) / (0.5 m)^2 = -2.16×10^6 N/C

To find the total electric field at the center of the square, we add up the electric fields due to each charge:

E_total = E₁ + E₂ = 2.16×10^6 N/C + (-2.16×10^6 N/C) = 0 N/C

Therefore, the magnitude of the electric field at the center of the square is 0 N/C.

Answer 2

4.30 x 10⁵ N/C

Step-by-step explanation:

Two positive +3.0-μC point charges at opposite corners of the square creates equal and opposite electric field at the center. hence the electric field by these two positive charges at opposite corners becomes zero.

`a` = length of the square of side = 0.50 m

`r` = distance of the center from each corner =
`(a)/(sqrt(2)) = (0.50)/(sqrt(2)) = 0.354 m`

Magnitude of net electric field at the center is given as

`E = (2kq)/(r^(2)) \\E = (2(8.99*10^(9))(3*10^(-6)))/((0.354)^(2)) \\E = 4.30*10^(5) NC^(-1)`