Lec16-3 - cture 16 cture 16 1 Magnetic field of a solenoid...

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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 Stretched-out 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. Biot-Savart’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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Lec16-3 - cture 16 cture 16 1 Magnetic field of a solenoid...

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