Question

A square conducting plate 51.0 cm on a side and with no net charge is placed in a region, where there is a uniform electric field of 81.0 kN/C directed to the right and perpendicular to the plate. (a) Find the charge density (in nC/m2) on the surface of the right face of the plate. -716850 nC/m2 (b) Find the charge density (in nC/m2) on the surface of the left face of the plate. 716850 nC/m2 (c) Find the magnitude (in nC) of the charge on either face of the plate. nC

Answer 1

Answer:

a)  $\sigma = 716.85nC/m^3$

b)  $\sigma = -716.85nC/m^3$

c) i) $Q = 198.157 nC$

ii) $Q = 198.157 nC$

Explanation:

To find the charge density on each face, let's use the formula: E=σ/εo

Where, E, electric field = 81.0 kN/C

εo =$8.85*10^-^1^2$

Thus, solve for σ

$\sigma = 81.0*10^3 * 8.85*10^-^1^2$

$\sigma = 7.1685*10^-^7 C/m^3$ or $\sigma = 716.85nC/m^3$

In charge density, the left face is negative  while on the right face it will be positive.

Therefore,

Charge density on the each face =

$- 716.85nC/m^3 and 716.85nC/m^3$

C) We'll first find the area of the square plate.

$A = (51.0*10^-^2)^2 = 0.2601m^2$

Use the formula below to find the magnitude of the charge on each surface of the plate:

On the right surface:

$Q = A\sigma$

$Q = 0.2601 * 761. 85$

$Q = 198.157 nC$

On the left surface:

$Q = A\sigma$

$Q = 0.2601 * -761. 85$

$Q = -198.157 nC$