Question

Consider two oppositely charged, parallel metal plates. The plates are square with sides L and carry charges Q and -Q. What is the magnitude of the electric field in the region between the plates

Answer 1

The magnitude of the electric field between two oppositely charged parallel plates can be calculated using the formula E = √((2Q/ε₀) / A), where Q is the charge on one plate, A is the area of the plates, and ε₀ is the permittivity of free space. The direction of the electric field is from the positive plate towards the negative plate.

Step-by-step explanation:

The magnitude of the electric field in the region between the plates can be determined using the formula E = √((Q/εο) / A), where Q is the charge on one of the plates, A is the area of the plates, and εο is the permittivity of free space. In this case, since the charges on the plates are equal in magnitude but opposite in sign, the magnitude of the electric field between them will be the same as if one plate had a charge of 2Q. Therefore, the formula becomes E = √((2Q/εο) / A).

For example, if the area of the plates is 0.75 m² and the charge on each plate is 0.225 C, the electric field between the plates can be calculated as follows:

E = √((2(0.225 C) / (8.85 x 10-12 C²/N·m²)) / (0.75 m²))

E ≈ 1.34 x 108 N/C

The direction of the electric field is from the positive plate towards the negative plate.

Answer 2

E =
`(Q)/(L^2 \epsilon_o)`

Step-by-step explanation:

For this exercise we use that the electric field is a vector, so the resulting field is

E_total = E₁ + E₂ (1)

since the field has the same direction in the space between the planes

Let's use Gauss's law for the electric field of each plate

Let's use a Gaussian surface that is a cylinder with the base parallel to the plate, therefore the normal to the surface and the field lines are parallel and the angle is zero so cos 0 = 1

Ф = ∫ .dA =
`q_(int)` /ε₀

if we assume that the charge is uniformly distributed on the plate we can define a charge density

σ = q_{int} A

as the field exists on both sides of the plate on the inside

E A = A σ / 2ε₀

E = σ / 2ε₀

we substitute in equation 1

E = σ /ε₀

for the complete plate

σ = Q / A = Q / L²

we substitute

E =
`(Q)/(L^2 \epsilon_o)`