Question

A long straight wire of a circular cross-section with radius \( a \) carries a steady current \( I \). The current is uniformly distributed across this cross-section. The plot of magnitude of magnetic field \( B \) with distance \( r \) from the centre of the wire is given by:

• A. \[ \text{Plot 1: } \] 
  
• B. \[ \text{Plot 2: } \] 
  
• C. \[ \text{Plot 3: } \]
  
• D. \[ \text{Plot 4: } \] 
  

Hint:

The magnetic field inside a current-carrying wire increases linearly with radius, while outside, the field decreases inversely with distance. Use this information to select the correct plot.

Answer 1

The Correct Option is C

For a long straight wire carrying a uniform current, Ampere's law dictates that the magnetic field outside the wire diminishes inversely with the radial distance from the wire (\( B \propto \frac{1}{r} \)). Conversely, inside the wire, the magnetic field escalates linearly with the distance from the central axis (\( B \propto r \)).

The accurate graphical representation depicts a magnetic field that exhibits a linear increase within the wire's radius and subsequently decreases inversely beyond this radius.

Final Answer: Plot 3.