Question

A thin, horizontal, 14-cm-diameter copper plate is charged to -2.6 nC . Assume that the electrons are uniformly distributed on the surface

1. What is the strength of the electric field 0.1 mm above the center of the top surface of the plate? Express your answer to two significant figures and include the appropriate units.

2. What is the direction of the electric field 0.1 mm above the center of the top surface of the plate? (Away/Toward)

3. What is the strength of the electric field at the plate's center of mass? Express your answer as an integer and include the appropriate units.

4. What is the strength of the electric field 0.1 mm below the center of the bottom surface of the plate? Express your answer to two significant figures and include the appropriate units.

5. What is the direction of the electric field 0.1 mm below the center of the bottom surface of the plate? (Away/Toward)

Answer 1

1.

electric field by a disk is given as

E = (2kQ/R²) [1 - a/sqrt(a² + R²)]

a = distance from the center = 0.1 mm = 0.1 x 10^-3 m

R = radius of disk = diameter/2 = 14 cm/2 = 7 cm = 0.07 m

E = (2kQ/R²) [1 - a/sqrt(a² + R²)]

inserting the values

E = (2 (9 x 10⁹) (2.6 x 10^-9)/(0.07)²) [1 - (0.1 x 10^-3)/sqrt((0.1 x 10^-3)² + 0.07²)]

E = 9.5 x 10³ N/C

2.

direction : towards the center

3.

electric field at center being equal and opposite from all side cancel out. hence electric field at center is zero.

4.

electric field by a disk is given as

E = (2kQ/R²) [1 - a/sqrt(a² + R²)]

a = distance from the center = 0.1 mm = 0.1 x 10^-3 m

R = radius of disk = diameter/2 = 14 cm/2 = 7 cm = 0.07 m

E = (2kQ/R²) [1 - a/sqrt(a² + R²)]

inserting the values

E = (2 (9 x 10⁹) (2.6 x 10^-9)/(0.07)²) [1 - (0.1 x 10^-3)/sqrt((0.1 x 10^-3)² + 0.07²)]

E = 9.5 x 10³ N/C

5)

towards the center