If a charge is enclosed by the surface of the sphere then total flux emitted from the surface will be:

Options

A. (the charge enclosed by surface)/`epsi_(0)`
B. (charge enclosed by surface) `epsi_(0)`
C. (charge enclosed by surface)/`4pi epsi_(0)`
D. 0

Answer

To solve the problem of determining the total electric flux emitted from the surface of a sphere when a charge is enclosed within it, we can use Gauss's Law. Here’s the step-by-step solution:

### Step 1: Understand Gauss's Law
Gauss's Law states that the total electric flux (Φ) through a closed surface is directly proportional to the charge (q) enclosed within that surface. Mathematically, it is expressed as:
\[ \Phi = \frac{q}{\epsilon_0} \]
where:
- \( \Phi \) is the electric flux,
- \( q \) is the charge enclosed,
- \( \epsilon_0 \) is the permittivity of free space.

### Step 2: Identify the Charge Enclosed
In this problem, we are given that there is a charge \( +q \) enclosed by the spherical surface.

### Step 3: Apply Gauss's Law
According to Gauss's Law, we can substitute the charge \( q \) into the formula for electric flux:
\[ \Phi = \frac{q}{\epsilon_0} \]

### Step 4: Conclusion
From our application of Gauss's Law, we find that the total electric flux emitted from the surface of the sphere is:
\[ \Phi = \frac{q}{\epsilon_0} \]
Thus, the correct answer is that the total flux emitted from the surface will be the charge enclosed by the surface divided by \( \epsilon_0 \).

### Final Answer
The total flux emitted from the surface will be:
\[ \frac{q}{\epsilon_0} \]