The electric field near the surface of a uniformly charged conducting plane can be determined by Gauss's law. If the plane is a square of sides 11.5 cm and carries a charge of 22.0 nC (that's nanocoulombs), what is the magnitude of the electric field near the surface?
To determine the magnitude of the electric field near the surface of a uniformly charged conducting plane, you can apply Gauss's law. Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed by that surface.
Here's how you can use Gauss's law to find the electric field:
Step 1: Determine the charge enclosed by the surface. In this case, the uniformly charged conducting plane is a square of sides 11.5 cm and carries a charge of 22.0 nC.
Step 2: Calculate the electric flux through a closed surface surrounding the plane. Since the conducting plane is uniform, the electric field will be constant and perpendicular to the surface.
Step 3: Apply Gauss's law, which states that the electric flux through a closed surface is equal to the product of the electric field and the area of the surface:
Electric Flux = Electric Field * Area
The area of the surface is given by the square's side length squared, so in this case, the area is (11.5 cm)^2.
Step 4: Rearrange the equation to solve for the electric field:
Electric Field = Electric Flux / Area
Plug in the values and calculate to find the magnitude of the electric field near the surface.