Question

Electric field in the figure is directed along x-axis ie. Ev 5AX+2B.
Where, E is in N/C, X in metre & AB are constants, A=10NC mand
BEIN NC m
Calculate-
(a) is E, flux passing through all the surfaces of the cube?
(b) determine E flux passing through M&N surfaces respectively.
(c) determine E. flux passing through the cube.
(d) determine the net charge enclosed within the cube.​

Answer 1

Given:

Electric field, Eₓ = 5Aₓ + 2B

Constant, A = 10 NC⁻¹ m⁻¹

Constant, B = 5 NC⁻¹ m⁻¹

To Find:

We have to find the electric flux through the cube and the net charge enclosed within the cube.

Solution:

The electric field directed along X direction is given as

                            Eₓ = 5Aₓ + 2B

The electric field at face M where x = 0 is E₁ = 2B

The electric field at face N where x= 10cm = 0·10 m is

E₂ = 5A× 0·10 + 2B = 0·5 A +2B

The electric flux through the face M is

φ₁ = $\[\overrightarrow {{E_1}} \cdot \overrightarrow {{S_1}} \]$ = E₁S₁ cosπ = -E₁S₁

    = -2B×I² where I = 0·01 m

∴ The electric flux through the face M is -2BI²

The electric flux through the face N is

φ₂ =  = E₂S₂ cos0 = ( 0·5A + 2B)I²

∴ The electric flux through the face N is ( 0·5A + 2B)I²

Net electric flux, φ = φ₁ + φ₂

        = -2BI² + ( 0·5A + 2B)I² = 0·5 AI²

        = 0·5 × 10 × 0·10²

        = 5 × 10⁻² Vm

∴ Net electric flux, φ = 5 × 10⁻² Vm.