Prove this equation using fields: show F=Bqv

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The discussion focuses on proving the equation F = Bqv using the relationship F = BIL and I = nAqv. Participants clarify that the number of charges in a wire segment can be expressed as N = nAL, linking it to the force equation. The conversation highlights difficulties in manipulating the equations and distinguishing between variables. Users seek assistance in simplifying the derivations to reach the desired equation. The overall tone reflects a sense of urgency and complexity in the problem-solving process.
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Homework Statement


Use equations F=BIl I=nAqv show F=Bqv, (help: the no. of particlees in a length l of wire cross-section area A is nAl, when the no. of particlees per unit volume is n)

Homework Equations


F=BIl I=nAqv F=Bqv

The Attempt at a Solution



F=B(nAqv)l
F=B(nnAlqv)l
F=B(n2Al2qv
F=B(n2Al2Itl/t
F=B(n2Al2Il
F=B(n2Al3I

I'm stuck after this, help asap appreciated.
 
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It is quite hard to distinguish small L from big i, fixed it below:

Given:
F=BIL
I=nAqv this should read NAqv where N is the total number of charges
number of charges N in a length L of wire cross-section area A is N = nAL, when the number of charges per unit volume is n

Can you give it another try now?
 
drmalawi said:
Can you give it another try now?
I wouldn't put too much hope about now. This decade, maybe.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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