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.
E= Nd Φ/dt but N=1 so E= dΦ/dt
The Attempt at a Solution
The solution offered in the book:
dΦ = BdA
dΦ/dt=0.10*Area moved by the length of the wire in 1 second (??)
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.