Question

The figure shows, in cross section, three infinitely large nonconducting sheets on which charge is uniformly spread. The surface charge densities are ?1 = 3.64 µC/m2, ?2 = 3.10 µC/m2, and ?3 = -5.24 µC/m2, and distance L = 0.999 cm. What are the (a) x and (b) y components of the net electric field at point P?

Answer 1

given

surface charge densities are

$\sigma$₁ = 3.64 µC/m²,

= 3.64 X 10^-6 C/m²

$\sigma$₂ = 3.10 µC/m²,

= 3.1 X 10^-6 C/m²

and $\sigma$ ₃ = - 5.24 µC/m²,

= - 5.24 X 10^-6 C/m²

and

distance L = 0.999 cm

= 0.00999 m

using equation

E = $\sigma$ / 2$\varepsilon$_o

then E = ( $\sigma$ ₁ + $\sigma$ ₂ + $\sigma$ ₃ ) / 2$\varepsilon$_o

= ( 3.64 X 10^-6 + 3.1 X 10^-6 - 5.24 X 10^-6 ) / 2 X 8.85 X 10^-12

E = 84745.76 N/C

a )

X - component is at P is ZERO

E_x = 0 N/C

b )

Y - componentis

E_y = 84745.76 N/C j