Question

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a wire has been put in shape of curve r=a/cos x (1+ sin^2 x). the wire is infinite in length and carries a current I. calculate the magnetic field due to this current at origin. r and x are two dimensional polar co ordinates in the plane of the paper.

Answer 1

Answer:

Explanation:see photo attached for answer

Answer 2

$U_{0}$ / 4π  Idl sin∅/ r'2

The solution is solved below :

Biot-Savart Law:

• Currents that arise due to the motion of charges are the source of magnetic fields.

• When charges move in a conducting wire and produce a current I, the magnetic field at any point P due to the current can be calculated by adding up the magnetic field contribution, dB, from small segments of the wire d s.

• These segments can be thought of as a vector quantity having a magnitude of the length of the segment and pointing in the direction of the current flow. The infinitesimal currentsource can then be written as I d s.

• Let r denote the distance from the current source to the field point P, and the corresponding unit vector. The Biot-Savart law gives an expression for the magnetic field contribution, from the current source,

• rˆdB Id s

where µ 0 is a constant called the permeability of free space:

• µ π4 10 T m/A

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