draw the graph of magnetic field on axial line or axial distance of current carrying circular loop. plz plz help me answer this question
Answers
Explanation:
Magnitude of magnetic field
All current elements are at equal linear distance from point P. As a result, the magnitude of magnetic field at P due to any of the equal current elements is same.
đB1=đB2=…….
Direction of elemental magnetic field
Unlike enclosed angle (θ), linear distance (r) and magnitude of magnetic field, the direction of magnetic field due to current elements are not same. As such, we can not integrate Biot-Savart differential expression to determine net magnetic field at P. Let us investigate the direction of magnetic fields due to two diametrically opposite current elements. Let the circular wire lie in yz plane as shown in the figure.
Direction of elemental magnetic field
Magnetic field is perpendicular to plane formed by current length element and displacement vectors.
The current length vector dl1 and displacement vector r1 form a plane shown as plane 1 and the magnetic field due to current element, B1, is perpendicular to plane 1. Similarly, the current length vector dl2 and displacement vector r2 form a plane shown as plane 2 and the magnetic field due to current element, B2), is perpendicular to plane 2. Clearly, these magnetic fields are directed in three dimensional space. If we imagine magnetic fields due to other current elements of the circular wire, then it is not difficult to imagine that these elemental magnetic fields are aligned on the outer surface of a conic section and that they are not in same plane.
Direction of elemental magnetic field
Magnetic fields are aligned on the outer surface of a conic section.
Another important point to observe is that all elemental magnetic field vectors form same angle φ. This can be verified from the fact that B1 is perpendicular to AP and Px is perpendicular to OA. Hence, angle between B1 and Px is equal to angle between OA and AP i.e. φ with x-axis. By symmetry, we can see that all elemental magnetic field vectors form the same angle with x- axis.
Resolution of elemental magnetic field vectors and net magnetic field
We resolve magnetic field vectors along x-axis and perpendicular to it, which lies on a plane perpendicular to axis i.e a plane parallel to the plane of circular coil (yz plane) as shown in the figure. We have shown two pairs of diametrically opposite current elements. See that axial components are in positive x-direction. The perpendicular components, however, cancels each other for a diametrically opposite pair.
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