To find the net electric flux leaving the spherical surface, we need to calculate the electric field intensity (E) at every point on the surface and then calculate the flux through each small area element (dA) on the surface using the equation:

Φ = ∫∫ E · dA

where Φ is the net electric flux.

1. Electric Field Intensity:
The electric field intensity at any point on the surface of a charged sphere is given by:

E = k * Q / r²

where k is the Coulomb's constant (9 × 10^9 Nm²/C²), Q is the total charge on the sphere, and r is the distance from the center of the sphere to the point.

2. Total Charge on the Sphere:
The total charge on the sphere can be calculated using the charge density (D) and the volume (V) of the sphere:

Q = D * V

where D is given as x C/m² and V can be calculated using the formula for the volume of a sphere:

V = (4/3) * π * r³

3. Electric Field Intensity Calculation:
Substituting the formula for the total charge into the equation for electric field intensity, we get:

E = k * (D * V) / r²

Substituting the values given in the question:
D = x C/m²
r = 3 mm = 0.003 m
V = (4/3) * π * (0.003)³ m³

4. Flux Calculation:
To calculate the flux, we need to find the dot product of the electric field and the differential area vector. Since the surface is a sphere, the electric field is radial and the area vector is also radial, so the dot product becomes:

E · dA = E * dA

The magnitude of the electric field at each point on the surface is the same, so we can take it out of the integral:

Φ = E ∫∫ dA

The integral of dA over the surface of a sphere is equal to the surface area of the sphere:

Φ = E * A

where A is the surface area of the sphere.

5. Surface Area Calculation:
The surface area of a sphere is given by the formula:

A = 4 * π * r²

Substituting the value of r into the equation, we get:

A = 4 * π * (0.003)² m²

6. Net Electric Flux Calculation:
Finally, substituting the values of E and A into the equation for flux, we get:

Φ = E * A

Substituting the values of E and A calculated in the previous steps, we can find the net electric flux leaving the spherical surface.

After evaluating the expression, the correct answer is option 'c' 113.1 nC.

No