lec20 - PEP112 Spring 2008 Prof. Svetlana Malinovskaya 31...

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PEP112 – Spring 2008 Prof. Svetlana Malinovskaya 31 March 2008 Solenoids, Magnetic Force
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The magnetic Field inside the Current-Carrying Wire • A wire of radius R carries current I. Find the magnetic field inside the wire at distance r<R from the axis. Assume the current density is uniform over cross section of the wire. • The magnetic field must be tangent to circles that are concentric with the wire. • To find the field strength at radius r, draw a circle of radius r. The amount of current passing through this circle is 2 2 2 2 , through circle through II IJ A r J J A R r R π == = = =
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2 00 2 2 0 0 22 0 , 2 2, , 2 2 through r Bd s I I R s BL rB I r rB I B r r R RR I B R μμ π μ πμ ⋅= = = == < = G G G G v v Continued. The magnetic field strength increases linearly with distance form the center of the wire until, at the surface of the wire, it matches the solution for the magnetic field outside the wire.
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The Magnetic Field of a Solenoid There are many applications for which we would like to generate a uniform magnetic field In practice, a uniform magnetic field is generated with a solenoid. We can think of a solenoid as a stack of current loops. Figure shows a single loop and a stack of three loops. The field inside is opposite to the field outside in a single loop. Loops reinforce field at the center of the loop 2 and cancel the field above and under the loop. With many current loops along the same axis, the field in the center is strong and roughly parallel to the axis, whereas the field outside the loops is very weak.
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• Magnetic field inside an ideal solenoid is uniform and parallel to the axis; the magnetic field outside is zero.
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lec20 - PEP112 Spring 2008 Prof. Svetlana Malinovskaya 31...

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