Question

Exercise 22.1 A flat sheet of paper of area 0.395 m2 is oriented so that the normal to the sheet is at an angle of 68 ∘ to a uniform electric field of magnitude 13 N/C .

Answer 1

I think questions are this

a) Find the magnitude of the electric flux through the sheet.

The flux of a uniform electric field "E" crossing a plane surface "A" at angle "theta" is;

Flux = EACos(theta)

Flux = (13)(0.395)Cos(68)

       = 1.924 N-m^2/C

b) Does the answer to part (a) depend on the shape of the sheet? Why or why not?

So long as the sheet is at the shape does not matter.

No.

For a plane surface the flux only depends on the area, not the shape.

c. For what angle Ф between the normal to the sheet and the electric field is the magnitude of the flux through the sheet largest

For a uniform electric field with magnitude E , the electric flux is

E = EA cos Ф

This is a maximum when cos Ф = 1 or Ф = 0 rad = 0.

So the electric flux is a maximum when Ф = 0

d) For what angle Ф between the normal to the sheet and the electric field is the magnitude of the flux through the sheet smallest?

For a uniform electric field with magnitude E , the electric flux is

ФE = EA cosФ

This is a minimum when cos Ф = 0 or Pi = 90 deg . So the electric flux is a minium when

Ф = 90 deg