Motional EMF Video Lessons

Concept

Problem: This problem explores how a current-carrying wire can be accelerated by a magnetic field. You will use the ideas of magnetic flux and the EMF due to the change of flux through a loop. Note that there is an involved follow-up part that will be shown once you have found the answer to Part B.A) What is the acceleration ar(t) of the rod? Take m to be the mass of the rod.Express your answer as a function of V, B, the velocity of the rod vr(t), L, R, and the mass of the rod m.

FREE Expert Solution

Induced emf:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbit{v}}{\mathbf{B}}{\mathbf{L}}}$

Ohm's law:

$\overline{){\mathbit{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{R}}}$

Magnetic force on a current-carrying conductor:

$\overline{){{\mathbf{F}}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{B}}{\mathbf{i}}{\mathbf{Lsin\theta }}}$

Newton's second law:

$\overline{){\mathbf{\Sigma }}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

Net emf, εnet = εapplied + εinduced = V + vBL

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Problem Details

This problem explores how a current-carrying wire can be accelerated by a magnetic field. You will use the ideas of magnetic flux and the EMF due to the change of flux through a loop. Note that there is an involved follow-up part that will be shown once you have found the answer to Part B.

A) What is the acceleration ar(t) of the rod? Take m to be the mass of the rod.

Express your answer as a function of VB, the velocity of the rod vr(t), LR, and the mass of the rod m.