Three infinite planes of constant surface charge density have been aligned perpe

Question

Three infinite planes of constant surface charge density have been aligned perpendicular to the x-axis, so they are all parallel to each other. Plane 1 is located at x1= - 0.3m and has surface charge density o1= +7.0 micro C/m. Plane 2 is located at x2 = 0.1m and has surface density o2= - 4.0 micro C/m. Plane 3 is located at x3 = 0.5m and has surface charge density o3= -3.0 micro C/m.

a.) what is the magnitude and direction of the electric field in between Planes 1 and 2?

b.) What is the magnitude and direction of the electric field in between Planes 2 and 3?

c.) What is the magnitude of the electric field outside of the plates?

Explanation / Answer

let
sigma1 = 7 micro C/m^2 at x1 = -0.3 m

sigma2 = -4 micro C/m^2 at x2 = 0.1 m

sigma3 = -3 micro C/m^2 at x3 = 0.5 m

a) In between 1st and 2nd sheets,

Enet = |E1| + E2| + |E3|

= sigma1/(2*peislon) + sigma2/(2*peislon) + sigma3/(2*epsilon)

= (sigma1 + sigma2 + sigma3)/(2*peislon)

= (7 + 4 + 3)*10^-6/(2*8.854*10^-12)

= 7.91*10^5 N/c (towards +x axis)

b)
In between 2nd and 3rd sheets,

Enet = |E1| - E2| + |E3|

= sigma1/(2*peislon) - sigma2/(2*peislon) + sigma3/(2*epsilon)

= (sigma1 - sigma2 + sigma3)/(2*peislon)

= (7 - 4 + 3)*10^-6/(2*8.854*10^-12)

= 3.39*10^5 N/c (towards +x axis)

c) ouside of the plates

E = |E1| - E2| - |E3|

= sigma1/(2*peislon) - sigma2/(2*peislon) + sigma3/(2*epsilon)

= (sigma1 - sigma2 - sigma3)/(2*peislon)

= (7 - 4 - 3)*10^-6/(2*8.854*10^-12)

= 0

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