Question

A uniformly charged conducting sphere is having radius 1m and surface charge density 20 c per m sq. The total flux leaving the Gaussian surface e5nclosing the sphere is

Answer 1

Final Answer : 80π/£°

where £° is permitivity in vacuum .

We know that,
Total Charge = Surface charged density * Surface area of sphere
= 20C/m^2 * 4π (1)^2
= 80π C

Now,
Total Flux by Gauss's law,
= 80π /£°

Answer 2

Answer:

The total flux leaving the Gaussian surface enclosing the sphere is 80π(∈₀)⁻¹.

Explanation:

The flux of a gaussian surface is calculated as,

$\phi=\frac{q}{\epsilon_o}$     (1)

Where,

Ф=a gaussian surface's flux

q=charge enclosed by the gaussian surface

∈₀=the permittivity of free space

From the question we have,

The surface charge density(σ)=20 C/m²

The radius of the sphere(r)=1m

We know,

$\sigma=\frac{q}{A}$     (2)

A=area of the sphere=4πr²

By placing all the values in equation (2) we get;

$20=\frac{q}{4\pi\times (1)^2}$

$q=4\pi\times 20$

$q=80\pi$     (3)

By placing the value of "q" in equation (1) we get;

$\phi=\frac{80\pi}{\epsilon_o}$

$\phi=80\pi(\epsilon_0)^-^1$

Hence, the total flux leaving the Gaussian surface enclosing the sphere is 80π(∈₀)⁻¹.

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