Question

A point charge of 5.1 μC is located at the center of a sphere with a radius of 7 cm. The Coulomb constant is 8.98755 × 10⁹ Nm²/C², and the acceleration of gravity is 9.8 m/s².

Determine the electric flux through the surface of the sphere.

Answer in units of N/C.

Answer 1

Given:

Charge q = 5.1 *10^-6 C

radius of the sphere r = (7 cm)(1m/100cm)

                                    = 0.07 m

coulomb constant K = 8.98755*10⁹ Nm²/C²

The magnitude of electric field everywhere on the surface of the sphere is

E = kq/r² ...........(1)

now the electric field is perpendicular to the spherical surface at all points on the surface. The electric

flux through the surface is EA.

Here A is the area of the surface of the sphere = 4πr²

^{Electric flux φ = EA}

                          ^{= (kq/r2 )( 4πr2 )}

                          = 4πkq

now plug the values in the above relation

φ = 4*(3.14)( 8.98755*10⁹ Nm²/C²)( 5.1 *10^-6 C)

    = 575.7*10³ Nm²/C