Magnetic monopoles cannot exist -

Options

A. true
B. false
C. may be true or false
D. nothing can be said

Answer

### Step-by-Step Solution:

1. **Understanding Magnetic Monopoles**:
- Magnetic monopoles refer to hypothetical particles that possess only one magnetic pole, either a North pole or a South pole, without the presence of the other. In contrast, all known magnets have both a North and a South pole.

2. **Existence of Magnetic Poles**:
- When a magnet is cut into smaller pieces, each piece will still have both a North and a South pole. This indicates that magnetic poles always exist in pairs.

3. **Theoretical Implications**:
- The concept of magnetic monopoles has been explored in theoretical physics, but no experimental evidence has been found to support their existence.

4. **Relation to Electric Charges**:
- Electric charges can exist as single entities (positive or negative), but magnetic poles cannot. This is due to the fundamental nature of magnetic fields, which are always produced by dipoles (pairs of poles).

5. **Gauss's Law for Magnetism**:
- According to Gauss's law for magnetism, the net magnetic flux through a closed surface is zero, which mathematically can be represented as ∮ B · dA = 0. This implies that there are no isolated magnetic charges (monopoles), as the magnetic field lines always form closed loops.

6. **Conclusion**:
- Based on the above points, it is concluded that magnetic monopoles cannot exist, and this statement is true.