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Unformatted text preview: cture 16 cture 16 1 Magnetic field of a solenoid • A constant magnetic field could be produced by an infinite sheet of current. In practice, however, it is easier and more convenient to use a solenoid . • A solenoid is defined by a current I flowing through a wire that is wrapped n turns per unit length on a cylinder of radius R and length L . L R Stretchedout solenoid cture 16 cture 16 2 Dipole Moments in Applied Fields app E ur Electric dipole app B ur p ur μ ur p ur p E ur μ ur B μ ur Magnetic Dipole External fields tend to align dipoles. B increases at center E decreases at center cture 16 cture 16 3 Potential Energy of Dipole • Work must be done to change the orientation of a dipole (current loop) in the presence of a magnetic field. • Define a potential energy U (with zero at position of max torque) corresponding to this work. ∫ ° ≡ θ τdθ U 90 ⇒ Therefore, [ ] θ θ μB U ° = 90 cos θ μB U cos = B x θ r F r F r μ . U = +μ B cos θ cture 16 cture 16 4 Reading Quiz 1 Three currents I 1 , I 2 , and I 3 are directed perpendicular to the plane of this page as shown. The value of the Ampere’s Law line integral of B∙ dl counterclockwise around the circular path is μ o 3I 1 What is the magnitude of the currents in I 2 and I 3 ? a. I 2 =0, I 3 can be any value b. I 2 =0, I 3 can only be zero c. I 2 =I 1 , I 3 can be any value d. I 2 =2I 1 , I 3 can be any value e. I 2 =0.5I 1 , I 3 can be any value I 1 I 3 I 2 cture 16 cture 16 5 Ampere’s Law in Magnetostatics The path integral of the dot product of magnetic field and unit vector along a closed loop, Amperian loop , is proportional to the net current encircled by the loop, t C C C B dl B dl I μ = = ∫ ∫ ur r g Ñ Ñ • Choosing a direction of integration. • A current is positive if it flows along the RHR normal direction of the Amperian loop, as defined by the direction of integration. BiotSavart’s Law can be used to derive another relation: Ampere’s Law 1 2 ( ) i i μ cture 16 cture 16 6 Magnetization and “Bound” Current in Matter • Ampere : Aligned magnetic moments in magnetized matter arise due to microscopic current loops inside the material. the material....
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 Fall '08
 Wei
 Current, Magnetic Field, Ture

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