Question

2.
If 1 coulomb charge is placed at the centre of a
cube of side 10 cm, calculate the flux coming out
of any face of the cube.
[Ans. 1.88 x 10^10Nm^2C^-1)
​

Answer 1

Answer:

189×10^8Nm^2C^-1

Explanation:

flux=1/6×8.8×10^-12

flux=189×10^8Nm^2C^-1

Answer 2

Answer:

The flux coming out of any face of cube is 1.883 x 10¹⁰ Nm²C⁻¹ .

Explanation:

• The electric flux through any surface is equal to the total number of electric field lines passing through that surface normally.
• From Gauss's law

$∫ E ds = \frac{q}{ε}$

• where, ∫ E ds is the total outward flux through the enclosed surface
• q is the total enclosed charge

Given that :

• Charge enclosed = 1 C
• side of cube, a = 10 cm = 0.1 m

Solution:

• Since, total flux through the cube by charge 1 C placed at the centre of cube is

$∅ = \frac{1}{ε}$

• A cube has 6 faces and area of each face is equal.
• Outward flux through any face of cube is

$∅ = \frac{1}{6ε} \\ = \frac{1}{6 \times 8.85 \times {10}^{ - 12} } \\ = 0.01883 \times {10}^{12} N{m}^{2} {C}^{ - 1} \\ = 1.883 \times {10}^{10} N{m}^{2} {C}^{ - 1}$

• Hence, flux through any face of cube is 1.883 x 10¹⁰ Nm²C⁻¹ .