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

[strick]

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.

 

[berkeman]

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...

 

[strick]

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.

 

[berkeman]

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.

 

[strick]

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.

 

[strick]

can anyone please help?