Two very Urge plastic sheets have uniform charge densities s

Two very Urge plastic sheets have uniform charge densities sigma_1, sigma_2, sigma_3, and sigma_4 as shown in the figure. What is the magnitude and direction of the electric field \'V at points A, B, and C?

Solution

At point  A, the electric field due to two non conducting sheets is,

E   = (1/2_0) (   - _ 1   + _2  + _3 + _ 4   )

=  (1/2*8.85*10^-12) ( -5 + 3+ 2 + 3) C/m^2

      = (1/2*8.85*10^-12) ( -5 + 3+ 2 + 3)x10^-6 C/m^2

= 1.7x10^5 N/ C , towards left

At a point B, the electric field is,

      E   = (1/2_0) (    _ 1   - _2  + _3 + _ 4   )

=  (1/2*8.85*10^-12) ( 5-3+2+3) C/m^2

          = (1/2*8.85*10^-12) ( 5-3+2+3)x10^-6 C/m^2

          = 3.95 *10^5 N/C, towards left

At a point C, the electric field is,

E   = (1/2_0) (   - _ 1   + _2  + _3 - _ 4   )

=  (1/2*8.85*10^-12) ( -5+3+2-3) C/m^2

      = (1/2*8.85*10^-12) (-5+3+2-3)x10^-6 C/m^2

     = -1.7 *10^5 N/C, towards left

magnitude: 1.7 *10^5 N/C, towards left