- #1
Gyroscope
Homework Statement
Would someone, please, show me that, if there is no current inside, that:
[tex]\oint \vec B \cdot d\vec l=0[/tex]
Please. Thanks.
Understanding Ampère's Law: How to Solve for Zero Current in a Closed Loop
- Thread starter Gyroscope
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- Ampere's law Law
In summary, Ampère's Law is a principle in electromagnetism that states that the magnetic field around a closed loop is directly proportional to the electric current passing through the loop. This law can be used to solve for zero current in a closed loop by setting up an integral equation and using the properties of the loop to simplify the equation. By solving for the current, one can determine the necessary conditions for zero current to occur in the loop, such as the presence of a magnetic field or the absence of a changing electric field. Overall, understanding Ampère's Law is crucial for analyzing and predicting the behavior of magnetic fields in closed loops.
Would someone, please, show me that, if there is no current inside, that:
[tex]\oint \vec B \cdot d\vec l=0[/tex]
Please. Thanks.
- #2
marcusl
Science Advisor
Gold Member
- 2,847
- 534
You can do this yourself! First use Stokes's theorem to relate your integral to a surface integral over curl(B), then substitute Maxwell's eqn. for curl(B). Note what happens if J and dD/dt are zero.
- #3
Gyroscope
I do not know Stokes Theorem. :) I am preparing to IPHO.
Related to Understanding Ampère's Law: How to Solve for Zero Current in a Closed Loop
1. What is Ampère's Law?
Ampère's Law is a fundamental principle in electromagnetism that describes the relationship between electric currents and the magnetic fields they produce. It states that the magnetic field around a closed loop is directly proportional to the electric current passing through the loop.
2. How do you solve for zero current in a closed loop using Ampère's Law?
To solve for zero current in a closed loop using Ampère's Law, you must first determine the total current passing through the loop. Then, you can use the equation B = μ₀I/2πr to calculate the magnetic field at any point along the loop. If the magnetic field is equal to zero at all points along the loop, then the current passing through the loop must be zero.
3. Can Ampère's Law be applied to any closed loop?
Yes, Ampère's Law can be applied to any closed loop, regardless of its shape or size. However, the loop must be completely closed and must not contain any gaps or breaks.
4. What is the significance of solving for zero current in a closed loop?
Solving for zero current in a closed loop is significant because it allows us to determine if the loop is electrically neutral. This information can be useful in understanding the behavior of electric circuits and in designing electrical systems.
5. Are there any limitations to Ampère's Law?
While Ampère's Law is a powerful tool for understanding the relationship between electric currents and magnetic fields, it does have some limitations. It only applies to steady currents, and it does not take into account the effects of changing electric fields. Additionally, it is only accurate in certain situations and may not accurately describe the behavior of materials with non-linear magnetic properties.
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