solve A thin square conducting plate430 cm on a side lies in

solve

A thin, square, conducting plate43.0 cm on a side lies in the xy plane. A total charge of 4.10 times 10^2 C is placed on the plate You may assume the charge density is uniform. find the charge on each face of the plate. What is the definition of surface charge density?/m^2 Find the electric field just above the plate. What is the equation for the electric field due to uniform surface charge? N/C. Find the electric field just below the plate. What sign must the magnitude of the field have? N/C

Solution

the charge density on each face of the plate is,

     p = (1/2)q/A = (1/2)(4.10X10^-8)/(0.43*0.43) = 1.1087e-7 = 11.087e-8 C/m^2

the electric field above the plate is,

   E = p/e0 = [11.087e-8]/[8.85x10^-12] = 12.5x10³ N/C, upward

the electric field below the plate is,

E = -p/e0 = -[11.087e-8]/[8.85x10^-12] = -12.5x10³ N/C

magnitude: 12.5x10³ N/C    direction: downward