Biot-Savart law and Ampere's law

  • Thread starter slayer1337
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  • #1
slayer1337
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1. An electric circuit consists of two long straight sections connecting a loop of radius r. The gap in the loop where the straight sections are connected subtends an angle of theta=60d, as shown in this figure (http://imgur.com/tseDHL6). Determine the magnetic field B at the point P in the centre of the loop, if a current I is flowing through the circuit.

See the diagram here - http://imgur.com/tseDHL6

2. Biot-Savart Law



3. The Attempt at a Solution - http://imgur.com/QFrlSn7

I have found the equation relating to the full loop but don't know how to do it for the missing segment.
 

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Answers and Replies

  • #2
BvU
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What's wrong with integrating ##d l\over r^2## ?
 
  • #3
maajdl
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You need to use the Biot-Savart law:

7463d12e92a79b39f6b3ac7d44dfe1be.png
 
  • #4
BvU
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Ma is right, but the next step is to convert to integrating ##d l\over r^2## because there is only one component left over; the others cancel.
 
  • #5
Rellek
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[itex]\int rd θ/r^2/[/itex]
 
  • #6
rude man
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Consider finding the field as though the circular section wasn't there, but the wire was continuous from -infinity to +infinity: B1. Can use ampere's law.

Then, use Biot-Savart to compute the field due to a short section of wire connecting the loose ends of the loop: B2.

Then, use Biot-Savart to compute the field due to the loop: B3.

B = B1 - B2 + B3.
 

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