Differentiate between statically and dynamically induced emf. A conductor of length
Sm moves in a uniform magnetic field of flux density 1. IT a: a velocity of 30m/s.
Calculate the emf induced in the conductor if üic direction of more of the conductor is
inclined at 600 to the direction of field.
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Answers
Figure 1. (a) A motional emf = Bℓv is induced between the rails when this rod moves to the right in the uniform magnetic field. The magnetic field B is into the page, perpendicular to the moving rod and rails and, hence, to the area enclosed by them. (b) Lenz’s law gives the directions of the induced field and current, and the polarity of the induced emf. Since the flux is increasing, the induced field is in the opposite direction, or out of the page. RHR-2 gives the current direction shown, and the polarity of the rod will drive such a current. RHR-1 also indicates the same polarity for the rod. (Note that the script E symbol used in the equivalent circuit at the bottom of part (b) represents emf.)
To find the magnitude of emf induced along the moving rod, we use Faraday’s law of induction without the sign:
emf
=
N
Δ
Φ
Δ
t
.
Here and below, “emf” implies the magnitude of the emf. In this equation, N = 1 and the flux Φ = BA cos θ. We have θ = 0º and cos θ = 1, since B is perpendicular to A . Now ΔΦ = Δ(BA) = BΔA, since B is uniform. Note that the area swept out by the rod is ΔA = ℓΔx. Entering these quantities into the expression for emf yields
emf
=
B
Δ
A
Δ
t
=
B
ℓ
Δ
x
Δ
t
.