Gauss's law in magnelism ensures that

Options

A. Magnetic monopoles do not exist
B. magnetic field lines from closed loops
C. Magnetic fields is conservative
D. Both (1) & (2)

Answer

To solve the question regarding Gauss's law in magnetism, we need to analyze what the law states and its implications. The question asks what Gauss's law in magnetism ensures.

### Step-by-Step Solution:

1. **Understanding Gauss's Law in Magnetism**:
Gauss's law in magnetism is one of Maxwell's equations, which states that the total magnetic flux through a closed surface is zero. Mathematically, it is expressed as:
\[ \oint \mathbf{B} \cdot d\mathbf{A} = 0 \]
where \(\mathbf{B}\) is the magnetic field and \(d\mathbf{A}\) is the differential area vector on the closed surface.

**Hint**: Recall that the integral of the magnetic field over a closed surface gives zero, indicating a balance of field lines entering and exiting.

2. **Implication of the Law**:
The implication of this law is that for every magnetic field line that enters a closed surface, there is an equal number that exits. This means that magnetic field lines do not begin or end at any point in space, which leads to the conclusion that there are no isolated magnetic charges (monopoles).

**Hint**: Think about what it means for field lines to enter and exit a surface. If they always balance, what can you say about the existence of magnetic monopoles?

3. **Magnetic Monopoles**:
Since there are no net magnetic charges within any closed surface, it implies that magnetic monopoles do not exist. In contrast to electric charges, which can be isolated, magnetic poles always come in pairs (north and south).

**Hint**: Consider the analogy with electric charges. If you can have a positive charge alone, what does that imply for magnetic charges?

4. **Conservative Nature of Magnetic Field Lines**:
The fact that magnetic field lines form closed loops also indicates that the magnetic field is conservative. This means that the work done in moving a magnetic pole around a closed path is zero.

**Hint**: Reflect on the concept of conservative fields in physics. What does it mean for the work done around a closed loop?

5. **Conclusion**:
Based on the analysis, we can conclude that Gauss's law in magnetism ensures two things:
- Magnetic monopoles do not exist.
- Magnetic field lines form closed loops.

Therefore, the correct answer to the question is **Option D: both 1 and 2**.

### Final Answer:
Gauss's law in magnetism ensures that magnetic monopoles do not exist and that magnetic field lines form closed loops. Thus, the correct option is D (both 1 and 2).