- #1
Mdhiggenz
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- 1
Homework Statement
I already worked out the right hand side. What is giving me problems is figuring out the left hand side, ∫Bdl
Since B is uniform, it can be removed from the integral leaving B∫dl
now I'm stuck.
Integrating a Uniform Magnetic Field: Solving for ∫Bdl
- Thread starter Mdhiggenz
- Start date
In summary, the student is struggling with finding the left hand side of the equation ∫Bdl, but has successfully simplified it to B∫dl by removing the uniform term B. They are now stuck and unsure of how to continue, but another contributor suggests that ∫dl is equal to the sum of all elements of length around a circle with radius R. The student confirms this and thanks the contributor for their help.
I already worked out the right hand side. What is giving me problems is figuring out the left hand side, ∫Bdl
Since B is uniform, it can be removed from the integral leaving B∫dl
now I'm stuck.
- #2
TSny
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Mdhiggenz said:
∫dl is just the sum of all the elements of length around the circle of radius R. Your work up to this point looks good to me.
- #3
Mdhiggenz
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in that case would it simply be 2pir?
- #4
TSny
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Yes, with r = R.
- #5
Mdhiggenz
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Thanks TSny.
1. What is a moving charged particle?
A moving charged particle is a particle that has an electric charge and is in motion. This could refer to any type of particle, such as an electron, proton, or ion, that has a net electric charge and is moving through space.
2. How does a moving charged particle create a magnetic field?
When a charged particle moves, it creates a magnetic field around it. This is because the particle's electric charge is in motion, and any moving electric charge produces a magnetic field. The strength and direction of the magnetic field depend on the velocity of the particle and the amount of charge it carries.
3. What is the relationship between a moving charged particle and an electric current?
An electric current is the flow of charged particles, such as electrons, through a conductor. When a charged particle is in motion, it can contribute to the overall electric current in a circuit. The faster the particle moves, the more current it will produce.
4. How does a moving charged particle behave in a magnetic field?
A moving charged particle will experience a force when placed in a magnetic field. This force, known as the Lorentz force, is perpendicular to both the velocity of the particle and the direction of the magnetic field. The magnitude of the force depends on the charge and velocity of the particle, as well as the strength of the magnetic field.
5. Can a moving charged particle change its direction in a magnetic field?
Yes, a moving charged particle can change its direction in a magnetic field. This is due to the force it experiences from the magnetic field, which causes it to follow a curved path. The direction of the force and resulting path can be determined using the right-hand rule, where the thumb points in the direction of the particle's velocity, the index finger points in the direction of the magnetic field, and the middle finger points in the direction of the resulting force.
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