Question

Two parallel plates, each 9 cm on a side, are given equal and opposite charges of magnitude 4.5 C. The plates are 1.5 mm apart. What is the electric field at the center of the region between the plates?

Answer 1

To find the electric field at the center of the region between the plates, we can use Gauss's Law and the formula E = sigma / (2 * epsilon), where sigma is the surface charge density and epsilon is the permittivity of free space.

Step-by-step explanation:

To find the electric field at the center of the region between the plates, we can use Gauss's Law. Gauss's Law states that when the surface of a conductor is not too far from a point charge, the electric field intensity at any point outside the Gaussian surface is directly proportional to the charge and inversely proportional to the square of the distance from the point charge.

In this case, the plates are parallel and have equal and opposite charges. The electric field between the plates is uniform and directed from the positive plate to the negative plate. The magnitude of the electric field can be found using the formula:

E = sigma / (2 * epsilon)

Where sigma is the surface charge density and epsilon is the permittivity of free space. Plugging in the given values, we have:

E = (4.5 C) / (2 * 9 cm * 1.5 mm * (1 m / 100 cm)) = 0.05 N/C.