Question

A thick current-carrying cable of radius ‘R’ carries current ‘I’ uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance ‘r’ from the axis of the cable is represented by 

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is D

To solve this question, we need to understand the magnetic field variation inside and outside a thick current-carrying cable. The cable has a radius 'R' and carries a uniformly distributed current 'I'. We want to determine how the magnetic field 'B' varies with the distance 'r' from the axis of the cable.

According to Ampère's law, the magnetic field inside and outside a current-carrying conductor is given by: 

1. Inside the cable (r < R):
2. Outside the cable (r ≥ R):

Given these expressions, the graph for the magnetic field as a function of distance 'r' from the axis of the cable will increase linearly with 'r' for \((r \lt R)\) and decay as \(\frac{1}{r}\) for \((r \ge R)\).

Let's match this to the options provided in the question:

This option shows the correct linear increase within the cable followed by a decrease following \(\frac{1}{r}\) outside the cable.

Therefore, the correct option for the variation of the magnetic field \(B(r)\) with the distance 'r' is the one represented by the fourth option.