Question

5. EMF in loop from oscillating field The loop shown at right, with area a, is rotating about the z- axis with angular velocity \omega and starting angle \phi_0. Namely, the angle of the loop-face-normal with respect to the x-axis is given by \phi(t) = \omega t + \phi_0. The magnetic field is also oscillating at frequency \omega, so that \vec{B}(t) = B_0 \cos(\omega t + \alpha)\hat{x} . (a) Is it possible to choose \phi_0 and \alpha so that the induced emf is always zero? If so, how are \phi_0 and \alpha related? (b) In general, what is the emf \mathcal{E}(t)?

          5. EMF in loop from oscillating field
The loop shown at right, with area a, is rotating about the z-
axis with angular velocity \omega and starting angle \phi_0. Namely,
the angle of the loop-face-normal with respect to the x-axis
is given by \phi(t) = \omega t + \phi_0. The magnetic field is also
oscillating at frequency \omega, so that \vec{B}(t) = B_0 \cos(\omega t + \alpha)\hat{x} .
(a) Is it possible to choose \phi_0 and \alpha so that the induced emf
is always zero? If so, how are \phi_0 and \alpha related?
(b) In general, what is the emf \mathcal{E}(t)?

5. EMF in loop from oscillating field
The loop shown at right, with area a, is rotating about the z-
axis with angular velocity ωand starting angle ϕ0. Namely,
the angle of the loop-face-normal with respect to the x-axis
is given by ϕ(t) = ωt + ϕ0. The magnetic field is also
oscillating at frequency ω, so that B⃗(t) = B0 cos(ωt + α)x̂ .
(a) Is it possible to choose ϕ0 and αso that the induced emf
is always zero? If so, how are ϕ0 and αrelated?
(b) In general, what is the emf ℰ(t)?

Added by Natalie V.

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