Calculation of Change in Magnetic Flux Linkage Across a Wire

AI Thread Summary
The discussion focuses on calculating the induced electromotive force (e.m.f.) across a moving wire in a magnetic field using Faraday's law. The initial solution suggests using the formula E = dΦ/dt, where the change in magnetic flux is derived from the area covered by the wire. However, participants argue that this approach is misleading, as the wire itself does not experience a change in magnetic flux due to its constant area and the uniform magnetic field. Instead, they recommend using the Blv law, which is based on the Lorentz force, to calculate e.m.f. more accurately. The conversation emphasizes the importance of correctly applying these principles to avoid confusion in electromagnetic calculations.
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Homework Statement


A straight wire of length 0.20m moves at a steady speed of 3.0m/s at right angles to a magnetic filed of flux density 0.10T. Use Faraday's law to determine the e.m.f. induced across the ends of a wire.

Homework Equations


E= Nd Φ/dt but N=1 so E= dΦ/dt

The Attempt at a Solution


The solution offered in the book:

Φ=BA
dΦ = BdA
dΦ/dt=B*dA/dt
dΦ/dt=0.10*Area moved by the length of the wire in 1 second (??)
dΦ/dt=0.10*3.0*0.20=0.06

E=0.06V

Now I understand that since the conductor is moving in a magnetic field, electrons experience a force and a charge separation occurs giving rise to an e.m.f. across the wire... By Faraday's law, this e.m.f. is equal (in this case) to dΦ/dt but here's the problem... I do not see how a wire cutting a uniform magnetic field experiences a change in magnetic flux. Its area is constant and magnetic flux density is constant so the magnetic flux felt by the wire Φ=BA is constant. The solution used the area covered by the wire which seems to me very irrelevant.

Thanks in advance.
 
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Faraday refers to a loop, not a piece of wire. Draw an imaginary rectangular loop behind the wire, with the other end of the loop not in the B field, to get the answer using Faraday. dA/dt is the rate of change of the area in the loop covered by the flux. It can be + or -.

Actually, using Faraday with moving media such as your wire is dangerous. Better to use the Blv law based on the Lorentz force q v x B:
emf = Blv, l = length of wire, v = velocity of wire. Forget about loops.
 
rude man said:
Faraday refers to a loop, not a piece of wire. Draw an imaginary rectangular loop behind the wire, with the other end of the loop not in the B field, to get the answer using Faraday. dA/dt is the rate of change of the area in the loop covered by the flux. It can be + or -.

Actually, using Faraday with moving media such as your wire is dangerous. Better to use the Blv law based on the Lorentz force q v x B:
emf = Blv, l = length of wire, v = velocity of wire. Forget about loops.
I understand. Thank you sir
 
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