E x, total (right side of slab) = E x, total (left side of slab, between the sla

Question

Ex, total (right side of slab) =

Ex, total (left side of slab, between the slab and the sheet) =

A square conducting slab with 7 m sides carries a net charge of 84 mu C The slab is placed to the right of an infinite charged nonconducting plane that lies in the yz plane at x = 0. The charge density of the infinite nonconducting plane is 2.7 mu C C/m2. The faces of the slab are parallel to the plane. Find the sign and magnitude of the electric field on each side of the slab (far from its edges so edge effects can be ignored) and the charge density on each face. Ex, total (right side of slab) = Ex, total (left side of slab, between the slab and the sheet) = sigma (right side of slab) = sigma (left side of slab) =

Explanation / Answer

solution:

[sigma]per face = (q/A) / 2 = (84uC / (7m)^2) / 2 = 1.7143 uC/m^2

E= [sigma]per face/ epsilon= (1.7143uC/m^2) / (8.85*10^-12 C^2/N/m^2) = 0.19370621*10^6 N/C = 193706.21 N/C

Ex, total(right side of slab) = E1 + E2 (where E1 is electric field from slab, E2 is electric field from plane) = (193706.21 N/C + (305084.75N/C)/2 ) = 346248.58 N/C

E2 is electric field from plane = [sigma]plane / epsilon = (2.7uC/m^2) / (8.85*10^-12 C^2/N/m^2) = 0.30508475*10^6 N/C = 305084.75 N/C

Ex, total(left side of slab, between the slab and the sheet) = -E1 + E2 = (-193706.21N/C +(305084.75 N/C )/2) = -41163.8 N/C

charge density[sigma](right side of slab) = Ex(right side)*epsilon = (346248.58 N/C * 8.85*10^-12 C^2/N/m^2 ) = 3.064 uC/m^2

charge density[sigma](right side of slab) = Ex(left side)*epsilon = (41163.8 N/C * 8.85*10^-12 C^2/N/m^2 ) = 0.364299 uC/m^2

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