A thin, horizontal 20cm×20cm copper plate is charged with 1.7×10^10 electrons. Consider the electrons are uniformly distributed on the surface.
A. What is the strength of the electric field 0.1 mm above the center of the top surface of the plate?
E=____ N/C
B. What is the strength of the electric field 0.1 mm below the center of the bottom surface of the plate?
E=____ N/C
Please provide answers. Thank you so very much
To find the strength of the electric field at a point above or below the copper plate, we'll need to use the electric field equation:
E = k * Q / r^2
where:
E is the electric field strength,
k is the Coulomb's constant (9 x 10^9 N m^2/C^2),
Q is the total charge on the plate, and
r is the distance from the center of the charge to the point.
In this case, the copper plate has a total charge of 1.7 x 10^10 electrons. Since the electrons are uniformly distributed on the surface, the charge can be calculated using the elementary charge (e) and Avogadro's number (N_A) to find the total charge (Q):
Q = (number of electrons) * (elementary charge)
= (1.7 x 10^10) * (1.6 x 10^-19 C)
Now let's calculate the electric field at the given points:
A. Electric field above the center of the top surface:
In this case, the distance (r) is 0.1 mm = 0.0001 m.
Using the equation E = k * Q / r^2, we can plug in the values to find the answer:
E = (9 x 10^9 N m^2/C^2) * [(1.7 x 10^10) * (1.6 x 10^-19 C)] / (0.0001^2 m^2)
Solving this expression will give you the value of E in N/C.
B. Electric field below the center of the bottom surface:
For this case, the distance (r) is also 0.1 mm = 0.0001 m.
We can use the same equation E = k * Q / r^2 with the given values to find the answer:
E = (9 x 10^9 N m^2/C^2) * [(1.7 x 10^10) * (1.6 x 10^-19 C)] / (0.0001^2 m^2)
Solving this expression will give you the value of E in N/C.