Calculation of Change in Magnetic Flux Linkage Across a Wire

[UnknownGuy]

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.

 

[rude man]

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.

 

[UnknownGuy]

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