Question

What is the electric flux through a sphere that has a radius of 1.00 m and carries a charge of +4.00 µC at its center?

Answer 1

Answer:

4.52 x 10⁵ Nm²/C

Explanation:

The electric flux Ф through a sphere of surface area A in an electric field E is given by;

Ф = E x A     ----------------------(i)

But first, let's calculate the electric field (E) of the charge (Q) as follows;

E = k x $\frac{Q}{r^{2} }$         ---------------------(ii)

Where;

k = electric constant = 8.99 x 10⁹ Nm²/C²

r = radius of the sphere = 1.00m

Q = 4.00μC = 4.00 x 10⁻⁶C

Substitute these values into equation (ii) as follows;

E = 8.99 x 10⁹ x $\frac{4 X 10^{-6} }{1.00^{2} }$

E = 35.96 x 10³ N/C

Secondly let's calculate the surface area (A) of the sphere as follows;

A = 4 π r²       -----------------------(iii)

Where;

r = radius of the sphere = 1.0m

Take π = 3.142

Substitute these values into equation(iii) as follows;

A = 4 x 3.142 x 1.00²

A = 12.568 m²

Now let's calculate the electric flux through the sphere as follows;

Substitute the values of A and E into equation (i) as follows;

Ф = E x A

Ф = 35.96 x 10³ x 12.568

Ф = 451.94 x 10³

Ф = 4.52 x 10⁵ Nm²/C

Therefore the electric flux through the sphere is 4.52 x 10⁵ Nm²/C