Question

A point charge of 4 µC is located at the center of a sphere with a radius of 25 cm. Find the electric flux through the surface of the sphere. The Coulomb constant is 8.98755 × 109 N · m2 /C 2 and the acceleration due to gravity is 9.8 m/s 2 .Answer in units of N · m2 /C.

Answer 1

Ф = 4.5176x10⁵ N . m² / C

Step-by-step explanation:

In this case, we need to use two expressions in order to calculate the electric flux of the sphere.

First the Electric flux is calculated using this expression:

Ф = E * A (1)

Where:

E: Electric field

A: Area of the sphere

To get the electric field E, we use this expression:

E = K * q / r² (2)

If we replace (2) into (1) we have the following:

Ф = K * q * A / r² (3)

Finally, we need to know the expression to get the area of a sphere which is the following:

A = 4πr² (4)

Replacing into (3):}

Ф = K * Q * 4πr² / r² discarting r²:

Ф = K * Q * 4π (5)

Now, all we need to do is replace the given values and solve for the electric flux of the sphere:

Ф = 8.98755x10⁹ * 4x10⁻⁶ * 4 * π

Ф = 4.5176x10⁵ N . m² / C

Hope this helps