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Maxwell's equation oint vecB * d vecs = ...

Maxwell's equation `oint vecB * d vecs = 0` says

A

a. Monopole can exist

B

b. Only dipole can exist

C

c. Magnetic field lines are closed loop

D

d. Net flux through surface is zero

Text Solution

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The correct Answer is:
To solve the question regarding Maxwell's equation `oint vecB * d vecs = 0`, we need to analyze what this equation implies about magnetic fields and their properties. ### Step-by-Step Solution: 1. **Understanding the Equation**: The equation `oint vecB * d vecs = 0` represents a line integral of the magnetic field vector `vecB` around a closed loop. This means that when we take the integral of the magnetic field along a closed path, the result is zero. **Hint**: Recall that a line integral around a closed loop gives information about the circulation of a vector field. 2. **Implication of the Equation**: The fact that this integral equals zero indicates that there are no net magnetic field lines passing through the loop. This is a fundamental property of magnetic fields, which suggests that magnetic field lines do not begin or end at any point (unlike electric field lines). **Hint**: Consider the nature of magnetic field lines and how they differ from electric field lines. 3. **Monopoles vs. Dipoles**: The equation implies that magnetic monopoles (isolated north or south poles) cannot exist. If they did, we would expect to see a net flux through the surface formed by the closed loop, which contradicts the equation. **Hint**: Think about how monopoles would affect the magnetic field lines and the implications for the line integral. 4. **Closed Loop Nature of Magnetic Field Lines**: Since the integral is zero, it reinforces the idea that magnetic field lines are closed loops. They do not start or end at any point but rather loop back on themselves. **Hint**: Visualize how magnetic field lines behave in space and how they connect back to themselves. 5. **Evaluating the Options**: - **Option A**: "Monopole can exist" - This is incorrect because the equation shows that monopoles cannot exist. - **Option B**: "Only dipole can exist" - This is also incorrect; while dipoles are present, the statement is misleading as it implies exclusivity. - **Option C**: "Magnetic field lines are closed loops" - This is correct, as established from the analysis. - **Option D**: "Net flux through the surface is 0" - This is misleading; while the integral is zero, it does not imply that the net flux through any arbitrary surface is zero. **Hint**: Carefully analyze each option in light of the implications of the equation. 6. **Conclusion**: The correct interpretation of the equation `oint vecB * d vecs = 0` leads us to conclude that magnetic field lines are indeed closed loops. Therefore, the correct answer is Option C. ### Final Answer: The correct answer is **C: Magnetic field lines are closed loops**.
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