An infinite sheet of charge is located in the yz plane at x

An infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge denisity ₁ = 0.45 C/m². Another infinite sheet of charge with uniform charge density ₂ = -0.64 C/m² is located at x = c = 36 cm.. An uncharged infinite conducting slab is placed halfway in between these sheets ( i.e., between x = 16 cm and x = 20 cm).

1)

What is E_x(P), the x-component of the electric field at point P, located at (x,y) = (8 cm, 0)?

N/C

2)

What is _a, the charge density on the surface of the conducting slab at x = 16 cm?

C/m²

3)

What is V(R) - V(P), the potentital difference between point P and point R, located at (x,y) = (8 cm, -20 cm)?

V

4)

What is V(S) - V(P), the potential difference between point P and point S, located at (x,y) = (28 cm, -20 cm)?

V

5)

What is E_x(T), the x-component of the electric field at point T, located at (x,y) = (44 cm, -20 cm)?

N/C

Solution

1)

Ex(P) = (sigma1 + sigma2)/(2*epsilon)

= (0.45 + 0.64)*10^-6/(2*8.854*10^-12)

= 61581.92 N/C

2)

sigma_a = -(0.45 + 0.64)*10^-6/2 = -0.545*10^-6 C/m^2 = -0.545 C/m^2

3) VR - VP = 0

4) VS - Vp = -E*d = -[61581.92]*(0.28 - 0.08 - 0.04) = -9853.1 V

5)

Ex(T) = (sigma1 - sigma2)/(2*epsilon) = (0.64 - 0.45)*10^-6/(2*8.854*10^-12) = 10734.46 N/C