Explain the function and components of circular loop.
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Answer:
gnetic Field of a Current Loop
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The circular loop of Figure has a radius R, carries a current I, and lies in the xz-plane. What is the magnetic field due to the current at an arbitrary point P along the axis of the loop?
Figure shows a circular loop of radius R that carries a current I and lies in the xz-plane. Point P is located above the center of the loop. Theta is the angle formed by a vector from the loop to the point P and the plane of the loop. It is equivalent to the angle formed by the vector dB from the point P and the y axis.
Determining the magnetic field at point P along the axis of a current-carrying loop of wire.
We can use the Biot-Savart law to find the magnetic field due to a current. We first consider arbitrary segments on opposite sides of the loop to qualitatively show by the vector results that the net magnetic field direction is along the central axis from the loop. From there, we can use the Biot-Savart law to derive the expression for magnetic field.
Let P be a distance y from the center of the loop. From the right-hand rule, the magnetic field dB⃗ at P, produced by the current element Idl⃗ , is directed at an angle θ above the y-axis as shown. Since dl⃗ is parallel along the x-axis and rˆ is in the yz-plane, the two vectors are perpendicular, so we have
dB=μ04πIdlsinθr2=μ04πIdly2+R2
where we have used r2=y2+R2.
Now consider the magnetic field dB⃗ ′ due to the current element Idl⃗ ′, which is directly opposite Idl⃗ on the loop. The magnitude of dB⃗ ′ is also given by Equation, but it is directed at an angle θ below the y-axis. The components of dB⃗ and dB⃗ ′ perpendicular to the y-axis therefore cancel, and in calculating the net magnetic field, only the components along the y-axis need to be considered. The components perpendicular to the axis of the loop sum to zero in pairs.
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