Two non-conducting infinite planes of uniform surface charge sigma_1 = 17.75mu C

Question

Two non-conducting infinite planes of uniform surface charge sigma_1 = 17.75mu C/m^2 and sigma_2 = -4.7 mu C/m^2 are parallel to each other and d = 0.855 m apart. What is the electric field between the planes? (Note: the field is positive if it is in the direction of x.) What is the electric field outside the planes, at A? Uniform electric field of strength E = 3.70 times l0^4 N/C is observed in the region adjacent to a large, flat, uniformly charged plate (see Fig. A). What is the charge per unit area on this plate?

Explanation / Answer

here,

charge density,
c1 = 17.75 uC/m^2 = 17.75*10^-6 C/m^2
c2 = -4.7 uC/m^2 = -4.7*10^-6 C/m^2

seperation distance, d = 0.855 m

Part A:
field between the plates,

E = c/2eo

where, eo is permitivity of freee space

E1 = 17.75*10^-6/(8.85*10^-12)
E1 = 2.00*10^6 N/C

due to second plate,
E2 = - (-4.7*10^-6)/(8.85*10^-12)
E2 = 5.31*10^6 N/C

Net field, E
E = E1 + E2
E = 2.00*10^6 + 5.31*10^6
E = 7.31*10^6 N/C

part B:
at point Field will be given as:

E = C2/eo
E = (-4.7*10^-6)/(8.85*10^-12)
E = -5.31*10^5 N/C

Question2 :
E = 3.70*10^4 N/C

Charge perunit are will be given as :

C = 2*E*eo
C = 2 * 3.70*10^4 * 8.85*10^-12
C = 6.549*10^-7 C/m^2

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