Question

Electric field `vecE` in a region is given by

`vecE = (5x^2 + 2)hati`

where E is in N/C and x is in meters.
A cube of side 10 cm is placed in the region as shown in figure.

Calculate

1. the electric flux through the cube, and
2. the net charge enclosed by the cube.

Answer 1

Here, x = 10 cm

= `10/100`m

= `1/10`m

The magnitude of the electric field at the left face,

`(5x^2 + 2)hati = (5 xx (0)^2 + 2)hati`

= `2 hati`

The magnitude of the electric field at the right face,

`E_R = (5x^2 + 2)hati`

= `(5 xx (1/10)^2 + 2)`

= `(5/100 + 2)`

E_R = 2.05 N/C

1. Φ = Φ_L + Φ_R

= E_LdS cos 180° + E_RdScos 0°

= `2 xx (1/10)^2 + 2.05 xx (1/10)^2`

= 5 × 10⁻⁴ Nm²C⁻¹

2. Charge, q = Φε₀ 

= 5 × 10⁻⁴ × 8.85 × 10⁻¹²

= 4.425 × 10⁻¹⁵