Question

Expression for an electric field is given by $\overrightarrow{ E }=4000 x^2 i \frac{ V }{ m }$ The electric flux through the cube of side $20 cm$ when placed in electric field (as shown in the figure) is ___$V cm$

Hint:

The electric flux is the product of the electric field and the area through which the field lines pass, considering the angle between the electric field and the area vector.

Answer 1

Correct Answer: 640

Solution:

The electric field is given by →E=4000x^2 i (V/m).

We need to find the electric flux through the cube of side 0.2 m (as 20 cm = 0.2 m).

Electric flux Φ through a surface is given by the formula:

Φ = ∫E • dA

Since E = 4000 x^2 i (V/m) acts along the x-axis, it will have non-zero contribution only on the faces perpendicular to x-axis.

Consider the two faces at x=0 and x=0.2.

• Face at x=0:
  The electric field E = 4000 × 0^2 = 0.
  No contribution to flux since the field is zero.
• Face at x=0.2:
  The electric field E = 4000 × (0.2)^2 = 160 V/m.
  Area dA = (0.2 × 0.2) = 0.04 m^2 with normal in positive x-direction.

Electric flux on this face:

Φ = E × dA = 160 × 0.04 = 6.4 V m

Convert to V cm:

Φ = 6.4 × (100^2) = 640 V cm

Verification: The computed flux 640 V cm falls in the range 640 to 640.

Conclusion: The electric flux through the cube is 640 V cm.