Question

A uniform electric field of magnitude 4.9 ✕ 10^4 N/C passes through the plane of a square sheet with sides 8.0 m long. Calculate the flux (in N · m^2/C) through the sheet if the plane of the sheet is at an angle of 30° to the field. Find the flux for both directions of the unit normal to the sheet.

1)unit normal with component parallel to electric field (N · m^2/C)
2)unit normal with component antiparallel to electric field (N · m^2/C)

Answer 1

1. 1.568 x 10^6 N m^2 / C

2. - 1.568 x 10^6 N m^2 / C

Step-by-step explanation:

E = 4.9 x 10^4 N/C

Side of square, a = 8 m

Area, A = side x side = 8 x 8 = 64 m^2

Angle between lane of sheet and electric field = 30°

Angle between the normal of plane of sheet and electric field,

θ = 90°- 30° = 60°

The formula for the electric flux is given by

`\phi = E A Cos\theta`

(1)
`\phi = E A Cos\theta`

By substituting the values, we get

Ф = 4.9 x 10^4 x 64 x Cos 60 = 1.568 x 10^6 N m^2 / C

(2)
`\phi = E A Cos\theta`

By substituting the values, we get

Ф = - 4.9 x 10^4 x 64 x Cos 60 = - 1.568 x 10^6 N m^2 / C