Motional Emf using Faraday's Law: Difference between revisions
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==The Main Idea== | ==The Main Idea== | ||
When a wire moves through an area of magnetic field, a current begins to flow along the wire as a result of magnetic forces. Originally, we learned to calculate the motional emf in a moving bar by using the equation <math>{\frac{q(vec{v} \times vec{B})L}{q}}</math> | When a wire moves through an area of magnetic field, a current begins to flow along the wire as a result of magnetic forces. Originally, we learned to calculate the motional emf in a moving bar by using the equation <math>{\frac{q(\vec{v} \times \vec{B})L}{q}}</math>. However, there's an easier way to do this: by writing an equation for emf in terms of magnetic flux. | ||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
We know that the magnitude of motional emf is equal to the rate of change of magnetic flux. <math>|emf| = \left|\frac{d\Phi_m}{dt}\right|</math> | |||
We also know that magnetic flux is defined by the formula: <math>\Phi_m = \int\! \vec{B} \cdot\vec{n}dA</math> | |||
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | ||
Revision as of 16:20, 30 November 2015
Claimed by Chelsea Calhoun
The Main Idea
When a wire moves through an area of magnetic field, a current begins to flow along the wire as a result of magnetic forces. Originally, we learned to calculate the motional emf in a moving bar by using the equation [math]\displaystyle{ {\frac{q(\vec{v} \times \vec{B})L}{q}} }[/math]. However, there's an easier way to do this: by writing an equation for emf in terms of magnetic flux.
A Mathematical Model
We know that the magnitude of motional emf is equal to the rate of change of magnetic flux. [math]\displaystyle{ |emf| = \left|\frac{d\Phi_m}{dt}\right| }[/math]
We also know that magnetic flux is defined by the formula: [math]\displaystyle{ \Phi_m = \int\! \vec{B} \cdot\vec{n}dA }[/math]
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
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