Question

Two infinite nonconducting sheets of charge are parallel to each other, with sheet A in the x = -2.15 plane and sheet B in the x = +2.15 m plane. Find the electric field in the region x < -2.15 m, in the region x > +2.15 m, and between the sheets for the following situations.

(a) when each sheet has a uniform surface charge density equal to +3.25 µC/m2 region (m) electric field (N/C)
x < -2.15 ________________

x > +2.15 ________________

-2.15 < x < +2.15 _________________

(b) when sheet A has a uniform surface charge density equal to +3.25 µC/m2 and sheet B has a uniform surface charge density equal to -3.25 µC/m2

region (m) electric field (N/C)
x < -2.15 __________________

x > +2.15 __________________

-2.15 < x < +2.15 _____________________

Answer 1

a) (-367231.63i , 367231.63i, 0) N/C

b) (0 , 0 , 367231.63i ) N/C

Step-by-step explanation:

a)

Case x < -2.15

`E =E_(+) + E_(+) \\E = 2*(sigma)/(2e_(0) ) = (sigma)/(e_(0) )\\\\E = (3.25*10^(-6))/(8.85*10^(-12) )\\\\E = - 367231.63 i`

Case x > 2.15

`E =E_(+) + E_(+) \\E = 2*(sigma)/(2e_(0) ) = (sigma)/(e_(0) )\\\\E = (3.25*10^(-6))/(8.85*10^(-12) )\\\\E = +367231.63 i`

Case -2.15 < x <+2.15

`E =E_(+) - E_(+) \\\\E = 0`

b)

Case x < -2.15

`E =E_(+) - E_(+) \\\\E = 0`

Case x > 2.15

`E =E_(+) - E_(+) \\\\E = 0`

Case -2.15 < x <+2.15

`E =E_(+) + E_(-) \\E = 2*(sigma)/(2e_(0) ) = (sigma)/(e_(0) )\\\\E = (3.25*10^(-6))/(8.85*10^(-12) )\\\\E = +367231.63 i`