A long hairpin is formed by bending a very long wire as shown in Fig. 30-43. If
ID: 2005297 • Letter: A
Question
A long hairpin is formed by bending a very long wire as shown in Fig. 30-43. If the wire carries a 20 A current, what are the direction and magnitude of B at point a and midpoint b? Take R = 9.0 mm and the distance between a and b to be much larger than R (each straight section is "infinite").
(a) Point a What is the direction?
1____________ T _____________2
(b) Midpoint b What is the direction?
3____________ T _____________
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Explanation / Answer
current through the wire is i = 20 A here we find the field by superposing the results of two semi infinite wires and a semi circular arc . magnetic field due to semi infinite straight wire B = o i / 4 R magnetic field at the center of circular arc is B = o i / 4 R where = rad a) magnitude of B at point a is Ba = 2 o i / 4 R + o i / 4R = o i /2 R ( 1/ + 1/2 ) = [ ( 4*10 -7 )( 20 ) / 2 R ] ( 1/ + 1/2 ) = 0.82 [ ( 4*10 -7 )( 20 ) / 2 (9*10-3 m ) ] = 1.144*10-3 T The direction of field is out of page b) b as a point mid way between two infinite wires magnitude of B at point b is Bb = 2 ( o i / 2R ) = o i / R = ( 4*10 -7 )( 20 ) / R = 8.88*10-4 T = 1.144*10-3 T The direction of field is out of page b) b as a point mid way between two infinite wires magnitude of B at point b is Bb = 2 ( o i / 2R ) = o i / R = ( 4*10 -7 )( 20 ) / R = 8.88*10-4 TRelated Questions
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