Question

A long cylindrical wire of radius R carries a uniform current I flowing through it. The variation of magnetic field with distance ‘r’ from the axis of the wire is shown by

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is C

The correct option is (C):
The magnetic field increases as the point moves closer to the boundary of the wire and decreases as it moves away from the boundary of the wire.

Answer 2

For a long cylindrical wire carrying a uniform current, the magnetic field at a distance \( r \) from the axis of the wire increases linearly with \( r \) inside the wire (for \( r < R \)), as given by Ampère's Law. Outside the wire (for \( r > R \)), the magnetic field decreases with \( 1/r \).

Therefore, the correct graph showing the variation of magnetic field \( B \) with distance \( r \) is option (A).

Answer 3

For a long straight cylindrical wire carrying a uniform current, the magnetic field at a distance \( r \) from the axis of the wire is given by Ampere's law. The magnetic field inside the wire (for \( r < R \)) increases linearly with distance from the center of the wire, while outside the wire (for \( r > R \)) it follows an inverse relationship with distance.

1. Inside the wire (for \( r < R \)):  
  The magnetic field increases linearly with distance \( r \), i.e., \( B \propto r \).

2. Outside the wire (for \( r > R \)):  
  The magnetic field decreases inversely with distance \( r \), i.e., \( B \propto \frac{1}{r} \).

Thus, the variation of the magnetic field is a linear increase inside the wire up to \( r = R \), and then it decreases inversely with \( r \) for \( r > R \).

Therefore, the correct graph that represents this variation is the one that shows a linear increase inside the wire and an inverse decrease outside the wire.

This corresponds to Graph (C).