A square plate of copper with 53.0 cm sides has no net charge and is placed in a region of uniform electric field of 77.0 kN/C directed perpendicularly to the plate. Find the charge density of each face of the plate.
The charges will be equal and opposite for the two faces. I suggest you apply Gauss' law to a "pillbox-shape" volume with one surface above the copper and one between the two surface of the copper.
There will be no E field coming out of the lower surface, because it is a conductor.
To find the charge density of each face of the plate, we need to calculate the total charge on each face of the plate and then divide it by the area of the respective face.
The formula for charge density is:
Charge density (σ) = Total charge (Q) / Area (A)
The total charge on each face of the plate can be found using the formula:
Total charge (Q) = Electric field (E) * Area (A)
Given:
Side length of the square plate (s) = 53.0 cm
Electric field (E) = 77.0 kN/C = 77.0 * 10^3 N/C
First, we need to convert the side length to meters:
Side length (s) = 53.0 cm = 53.0 * 0.01 m = 0.53 m
Now, to calculate the area of the square plate:
Area (A) = Side length (s) * Side length (s) = 0.53 m * 0.53 m
Now, we can find the total charge on each face of the plate:
Total charge (Q) = Electric field (E) * Area (A)
Substituting the given values:
Total charge (Q) = 77.0 * 10^3 N/C * (0.53 m * 0.53 m)
Calculate Q using the above expression.
Finally, divide the calculated total charge by the area of the respective face to find the charge density of each face:
Charge density (σ) = Total charge (Q) / Area (A)
Substitute the calculated values to find the charge density of each face of the plate.