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Electromotive force and conservation of energy

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Exercise

Physics Electricity Magnetism

https://texercises.com/exercise/electromotive-force-and-conservation-of-energy/

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Exercise:
Show that for a conductor moving through a uniform magnetic field the electric power dissipated in a resistor connected to the moving conductor is equal to the mechanical power required to keep the velocity of the conductor constant.

Solution:
The induced emf is given by calE v B ell The resultant current through the resistor is then I fracV_RR fraccalER fracv B ellR It follows for the power dissipated in the resistor sscPel V_R I calE I v B ell fracv B ellR fracleft v B ell right^R The force on the moving conductor in the magnetic field is F I ell B fracv B ellR ell B fracv B^ ell^R The mechanical power is therefore sscPmech F v fracv B^ ell^R v fracv B ell^R It follows that sscPel sscPmech

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Lecture Notes Magnetism by by

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Attributes & Decorations

Branches	Magnetism
Tags	conservation of energy, induction, power
Content image
Difficulty	(2, default)
Points	0 (default)
Language	(English)
Type	Show
Decoration