In a laboratory, a researcher rotates a non-circular conductive frame with variable angular speed through a spatially non-uniform magnetic field. Which outcome below most accurately describes how the induced electromotive force (emf) would behave during a complete rotation?
The emf will display irregular peaks and troughs reflecting both the changing angular speed and the field's spatial variation.
By Faraday's law, the induced emf equals the rate of change of magnetic flux: \(e = -\frac{d\Phi}{dt}\), where \(\Phi = \int \vec{B} \cdot d\vec{A}\).
For a frame rotating in a field, \(\frac{d\Phi}{dt}\) depends on how fast the angle changes (angular speed ω) and on how the flux varies with position.
A pure sinusoidal emf \(e = NBA\omega \sin \omega t\) arises only when the coil is a regular plane loop, the field is uniform and ω is constant.
Here ω varies, so the rate of flux change speeds up and slows down; the field is non-uniform and the frame is non-circular, so the flux changes unevenly with angle. The emf therefore shows irregular peaks and troughs.
A constant emf would need a steady rate of flux change, which a rotating frame cannot give. Zeros at regular intervals and a uniform sinusoid both require constant ω and a uniform field, neither of which holds here.
Hence, the answer is The emf will display irregular peaks and troughs reflecting both the changing angular speed and the field's spatial variation.
Similar Questions
A coil has 100 turns. If the magnetic flux linked with each turn changes by 0.05 Wb in 1 s, the induced emf is:
Important Questions from Faraday's Law
In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side.
List I
List II
1.
∇. D
P
0
2.
∇ × E
Q
\(\rho_v\)
3.
∇. B
R
\( - \frac{{\partial B}}{{\partial t}}\)
4.
∇ × H
S
\(J+ \frac{{\partial D}}{{\partial t}}\)
“By the motion of the conductor or the coil in a magnetic field, i.e., the magnetic field is stationary and the moving conductors cut through it. The EMF generated in this way is normally called dynamically induced EMF.”
The given statement is specified by which of the following laws?
A flux of 0.25 mWb is produced by a coil of 1000 turns wound on a ring with a current of 2 A in it. Calculate the e.m.f induced in the coil when a current of 10 A is switched off, assuming the current will fall to zero in 1 millisecond.
Which of the following law states that “whenever the magnetic flux linked with a conductor or coil changes, an emf is induced in it?
All induction type transducers are based on
