- #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
- Start date
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- Ampere's law Law
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SUMMARY
This discussion focuses on applying Ampère's Law to demonstrate that the line integral of the magnetic field around a closed loop is zero when there is no current present. The key steps involve using Stokes's theorem to convert the line integral into a surface integral of the curl of the magnetic field, followed by substituting Maxwell's equations. Specifically, when the current density (J) and the displacement current (dD/dt) are both zero, the integral evaluates to zero, confirming the statement.
PREREQUISITES- Understanding of Ampère's Law and its applications
- Familiarity with Stokes's theorem
- Basic knowledge of Maxwell's equations
- Concept of magnetic fields and current density
- Study Stokes's theorem in detail and its applications in electromagnetism
- Review Maxwell's equations, focusing on the implications of zero current density
- Explore examples of applying Ampère's Law in various scenarios
- Investigate the physical significance of magnetic fields in closed loops
Students preparing for physics competitions, educators teaching electromagnetism, and anyone seeking to deepen their understanding of magnetic fields and their mathematical descriptions.
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
- 2,968
- 687
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.
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