If there were only one type of charge of the universe then

Options

A. `oint_(s)vecE.dvecsne0` on any surface
B. `oint_(s)vecE.dvecs=0` if the charge is outside the surface
C. `oint_(s)vecE.dvecs=q/(epsilon_(0))` if charges of magnitude q were inside the surface
D. both (b) and ( c) are correct

Explanation

To solve the question, "If there were only one type of charge in the universe, then...", we need to analyze the implications of having only one type of electric charge based on the principles of electrostatics, particularly Gauss's Law.

### Step-by-Step Solution:

1. **Understanding Charge Types**:
- In our universe, we have two types of electric charges: positive and negative. If there were only one type of charge (let's say only positive charges), we need to consider how this would affect electric fields and forces.

**Hint**: Think about how electric fields are created and how they interact with charges.

2. **Applying Gauss's Law**:
- Gauss's Law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface. Mathematically, it is expressed as:
\[ \Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\varepsilon_0} \]
- Here, \( \Phi_E \) is the electric flux, \( \vec{E} \) is the electric field, \( d\vec{A} \) is the differential area vector, and \( Q_{enc} \) is the charge enclosed by the surface.

**Hint**: Remember that the electric field lines originate from positive charges and terminate at negative charges.

3. **Case 1: Charge Inside the Gaussian Surface**:
- If we consider a Gaussian surface that encloses a charge \( Q \) (which is positive), the electric flux through the surface would be given by:
\[ \Phi_E = \frac{Q}{\varepsilon_0} \]
- This indicates that there is a non-zero electric field due to the charge inside the surface.

**Hint**: Visualize how the electric field lines would behave if there were only positive charges.

4. **Case 2: Charge Outside the Gaussian Surface**:
- If the charge \( Q \) is outside the Gaussian surface, then the enclosed charge \( Q_{enc} = 0 \). According to Gauss's Law, the electric flux through the surface would be:
\[ \Phi_E = 0 \]
- This means that the electric field due to the external charge does not contribute to the flux through the closed surface.

**Hint**: Consider how the electric field behaves at points on the surface when there are no charges inside it.

5. **Conclusion**:
- From the analysis, we can conclude that if there were only one type of charge in the universe, the electric field would behave differently based on whether charges are inside or outside a Gaussian surface. The electric field would not cancel out completely, and we would always have a non-zero electric field from the enclosed charge.

**Final Answer**: If there were only one type of charge in the universe, the electric field would be non-zero when charges are inside a surface and zero when there are no charges inside.