Phys 0175 - Lecture 25

# Phys 0175 - Lecture 25 - Lecture 25(Mar 18 2009 Magnetic...

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Lecture 25 (Mar. 18, 2009): Magnetic Fields due to Currents (cont’d): Applications of Ampere’s Law (solenoid, toroid) Current-carrying coil acting as a magnetic dipole Illustrative examples

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Magnetic field produced by a solenoid: The magnetic field inside the solenoid becomes more uniform as the number of turns per unit length increases.
Apply Ampere’s Law to find the magnetic field inside a long solenoid with n turns per unit length: Therefore in the center of the solenoid: B = μ 0 in ( 29 0 0 b c d a b enc a b c d a B ds B ds B ds B ds B ds B ds Bh i i nh μ μ = + + + = = = = r r r r r r r r r r r r g g g g g g Ñ

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Variation of the magnetic field B at points along the axis of a solenoid of length 4a and diameter 2a:
A toroidal solenoid (aka toroid): In the center of the toroid, in the region enclosed by the coils: The magnetic field is zero inside (r<a) and outside (r>b). 0 0 2 iN B in r μ μ π = = a b

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Summary of magnetic field configurations:
(A) B at a distance r from the center of a long, straight conductor: (A)

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