# HW15soln - 28-44 A toroidal solenoid has inner radius 13.5...

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Physics 21 Fall 2007 Solution to HW-15 28-39 A long, straight, cylindrical wire of radius R carries a current uniformly distributed over its cross section. At what location is the magnetic field produced by this current equal to half of its largest value? Consider points (A) inside and (B) outside the wire. 28-41 A solenoid is designed to produce a magnetic field of mag- nitude B at its center. It has a radius of r and a length of L , and the wire can carry a maximum current of I . (A) What minimum num- ber of turns n per unit length must the solenoid have? (B) What total length of wire is required? 28-43 A magnetic field of 37.2 T has been achieved at the MIT Magnetic Laboratory. Find the current needed to achieve such a field (A) a distance r from a long, straight wire, (B) at the center of a circular coil of radius R that has N turns, and (C) near the center of a solenoid with radius r, length L , and N turns.
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Unformatted text preview: 28-44 A toroidal solenoid has inner radius 13.5 cm and outer radius 17.7 cm. The solenoid has N turns and carries a current of I . What is the magnitude of the magnetic field at distances r from the center of the torus such that (A) r is inside the torus, (B) r is in the center of the coils, and (C) r is greater than the outside radius of the torus? 28-47 A toroidal solenoid with 500 turns is wound on a ring with a mean radius of R . Find the current in the winding that is required to set up a magnetic field of magnitude B in the ring if the ring is made of (A) annealed iron ( K _m=1400) or (B) silicon steel ( K _m=5200). (A) (B) outside the wire: The maximum field is at the surface of the wire, r=R . For larger R , the field falls off as 1/R (Ampere's Law will show that the field is the same as that of a thin wire) , so the point where the field is half as large is at r =2 R ....
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## This note was uploaded on 02/29/2008 for the course PHYSICS 21 taught by Professor Hickman during the Spring '08 term at Lehigh University .

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