Question

Electric field in the figure is directed along x-axis ie. Ex = 5 AX+2B
Where, E is in N/C, X in metre & A,B are constants, A=10NC 'm and
B-5N NC mi.
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.
enclosed within the cube.​

Answer 1

Explanation:

Potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched. A steel ball has more potential energy raised above the ground than it has after falling to Earth.

Answer 2

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.