What Is the Resultant Magnetic Force on a Wire in a Magnetic Field?

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Homework Help Overview

The discussion revolves around calculating the resultant magnetic force on a wire carrying current in a magnetic field, specifically focusing on a wire with a central arc placed in a uniform magnetic field. Participants are tasked with expressing the force in terms of magnetic field strength, length, radius, and current.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to sum individual forces acting on the wire, noting the simplicity of the straight wire sections compared to the complexity of the arc. Questions arise about the cancellation of horizontal components and the setup of integrals for calculating forces.

Discussion Status

Some participants have provided guidance on integrating forces over the arc and have prompted others to clarify their setup of the integral. There is an ongoing exploration of the vertical resultant force and the use of the cosine rule in the context of the problem.

Contextual Notes

Participants express uncertainty about their approaches and the setup of equations, indicating a lack of clarity on how to proceed with the calculations. There are indications of imposed homework constraints, as participants seek help without revealing complete solutions.

strick
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Figure below shows a length of wire with a central arc, placed in a uniform magnetic field B that points out of the plane of the figure. If the wire carries a current i, what resultant magnetic force F acts on it? Express the answer in terms of B, L, R and i.


I am stuck in this question for more than 2 hours and have no idea on how to approach the question.

Please help. Thank you.
 

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strick said:
Figure below shows a length of wire with a central arc, placed in a uniform magnetic field B that points out of the plane of the figure. If the wire carries a current i, what resultant magnetic force F acts on it? Express the answer in terms of B, L, R and i.


I am stuck in this question for more than 2 hours and have no idea on how to approach the question.

Please help. Thank you.

You approach it by adding up the individual forces. The straight wire parts are easy, hopefully. The slightly harder part is integrating the force over the arc. What can you say about the horizontal components of force as you do the integration?

Please show us the integral you have set up for the arc...
 
i think the horizontal resultant force around the arc should cancel out, however, i m still stuck in setting up the equation for the vertical resultant force around the arc.
 
strick said:
i think the horizontal resultant force around the arc should cancel out, however, i m still stuck in setting up the equation for the vertical resultant force around the arc.

Correct about the horizontal cancellation. What integral equation do you use to calculate the force on a current in a magnetic field? Show us how you are starting to set up the integral.
 
F = BiL
I used the cosine Rule to express dL-> dL = (2Rsqu. - 2Rcos dθ)squ root
therefore dF at particular point = Bi(dL)/sinθ

But i think I am in a totally wrong direction.

I think i should set up a function so that the total area under the curve equals to the vertical force acting downwards. But i really have no idea where to start.
 
can anyone please help?
 

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