A circular loop of radius R carries a current I. At what distance along the axis of the loop isthe magnetic field one-half its value at the center of the loop?

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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A circular loop of radius R carries a current I. At what distance along the axis of the loop isthe magnetic field one-half its value at the center of the loop?

For a point along the y-axis of a circular current-carrying loop
21A
B =
4t (R? + y²)3/2
where R is the radius of the loop and A = TR.
For a point in the center:
Hol
B
2R
For a point a distance r away from an infinitely long straight current carrying wire
%3D
Но 21
4T r
B
In a similar way to how we derived the results above, you can derive the B-field at a point a distance
r away from the mid-point of a long straight current - carrying wire of length L:
IL
В
4t tVr2 + (L/2)²
where L is the length of the wire and I is the current in the wire.
The directions are given by the right-hand rule.
Transcribed Image Text:For a point along the y-axis of a circular current-carrying loop 21A B = 4t (R? + y²)3/2 where R is the radius of the loop and A = TR. For a point in the center: Hol B 2R For a point a distance r away from an infinitely long straight current carrying wire %3D Но 21 4T r B In a similar way to how we derived the results above, you can derive the B-field at a point a distance r away from the mid-point of a long straight current - carrying wire of length L: IL В 4t tVr2 + (L/2)² where L is the length of the wire and I is the current in the wire. The directions are given by the right-hand rule.
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