An infinite plane of surface charge density $\Sigma$ = +8.00 nC/m² lies in the yz plane at the origin, and a second infinite plane of surface charge density $\Sigma$= -8.00 nC/m² lies in a plane parallel to the yz plane at x = 4.00 m. The electric field at x = 3.50 m is approximately A) 226 N/C B) 339 N/C C) 904 N/C D) 452 N/C E) zero

Question

Quizplus · Accepted Answer

We can use the principle of superposition to find the net electric field at any point due to both of the planes. Since the two planes have opposite charges, their electric fields will also have opposite directions.

At x = 3.50 m, the distance from the first plane is 3.50 m and the distance from the second plane is 0.50 m, so the magnitude of the electric field due to each plane is:

E1 = σ/2ε0 = (8.00 nC/m)(1/m)(1/(2ε0)) = 2.25 × 10^6 N/C
E2 = -σ/2ε0 = -(8.00 nC/m)(1/m)(1/(2ε0)) = -2.25 × 10^6 N/C

The net electric field is the vector sum of E1 and E2, which gives:

E = E1 + E2 = 0.

Therefore, the electric field at x = 3.50 m is zero, and the best choice is E) zero.

An Infinite Plane of Surface Charge Density Σ\SigmaΣ = +800 NC/m2 Lies in the Yz Plane at the Origin

An Infinite Plane of Surface Charge Density $\Sigma$ = +800 NC/m² Lies in the Yz Plane at the Origin