Question

Consider a conducting sheet with dimensions 1m by 1m by 1mm. A charge of 1 C was deposited into it, assume it is spread uniformly along the surface.

1.19 [1pt] What is electric field inside the sheet?

1.19 ANSWER

1.20 [1pt] What is electric field immediately outside the sheet. Sketch the directions and indicate the magnitude.

1.20 ANSWER

1.21 [2pt] Suppose we place a positive point charge at a distance 1 mm away from the conducting sheet (around the center) in problem 1.19. Will the distribution of charges inside the sheet change? If it does, sketch how.

1.21 ANSWER

1.22 [1pt] Consider a sheet of paper with a thickness of 0.1 mm and a dielectric constant of 3. Suppose we would like to make a 1 F capacitor using this sheet as a spacer between two metallic plates. What should be the area of the sheet?

1.22 ANSWER

Answer 1

1.19 :

Electric field inside a conductor =0 , always , irrespective of the charge on the surface. E =0 inside the sheet.

1.20 :

surface charge density =1/2 = 0.5 C/sq.m , charge spreads on both surfaces uniformly

Electric field near a conducting sheet = /_o = 0.5/8.85E-12 = 5.65 E+10 N/C

1.21: Yes the +ve charge induces a -ve charge on the sheet , The induced charge is maximum at the center and becomes 0 at the edges. The charge charge distribution at the center takes a dip.

1.22 Capacitance C = K A₀/d = 1F

area of the paper A = 1/3 *0.1/ 8.85E-12 =  3.77E+9 sq.m