Question

Consider a uniform electric field E = 3 × 10³ `hat i` N/C.

1. What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?
2. What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

Answer 1

(a) Area of square, A = a² = 10² = 100 cm²

= 100 × 10^-4 m²

= 10⁻² m²

Since the plane lies on the y-z-axis, the area vector `vecA` points in the same direction.

i.e., `vecA = (10^-2  hati) m^2`

∴ Electric Flux through the square is:

Φ = `vecE · vecA` = `(3 xx 10^3  hati)*(10^-2  hati)`

= 3 × 10¹

or Φ = 30 V-m

(b) When normal to plane, i.e., `vecA` makes an angle of 60° with `vecE`, then

Φ' = EA cos 60°

= `3 xx 10^3 xx 10^-2 xx 1/2`

= 1.5 × 10¹

or Φ' = 15 V-m