A thick current carrying cable of radius carries current uniformly distributed across its cross-section. The variation of magnetic field due to the cable with the distance from the axis of the cable is represented by :
1
2
3
4
Official Solution
Correct Option: (3)
To solve the problem of the magnetic field variation inside a thick current-carrying cable, where the current is uniformly distributed across the cross-section, we will use the principles of magnetism and apply Ampere's Law.
Understanding the Problem:
We have a current-carrying cable with radius and a uniformly distributed current . We need to determine how the magnetic field changes with the distance from the cable's axis.
Theory and Formulae:
By Ampère's Law, the line integral of the magnetic field around a closed path is equal to times the current passing through the enclosed area:
Here, is the current enclosed by the path. For a radial distance , the magnitude of the magnetic field inside the cable can be derived as follows:
, the current enclosed by a circle of radius .
Thus,
Therefore,
Conclusion:
The magnetic field inside the cable increases linearly with the distance from the axis of the cable, and it is directly proportional to .
Hence, the correct option for the variation of magnetic field inside the cable versus the distance is as shown in the above diagram.
