Question

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is:
[A.] maximum at either end of the conductor
[B.] maximum at the axis of the conductor and minimum at the midpoint
[C.] minimum at the surface of the conductor
[D.] minimum at the axis of the conductor
[E.] same at all points in the cross-section of the conductor
Choose the correct answer from the options given below:

• A. D Only
• B. B, C Only
• C. A, D Only
• D. E Only

Hint:

Inside a current-carrying conductor with uniform current density, magnetic field increases linearly with distance from the axis.

Answer 1

The Correct Option is A

Concept: For a long straight conductor of radius \(R\) carrying uniformly distributed current \(I\), the magnetic field inside the conductor \((r<R)\) is given by: \[ B(r)=\frac{\mu_0 I r}{2\pi R^2} \]
Step 1: Behaviour of magnetic field From the expression: \[ B \propto r \]
At the axis of the conductor \((r=0)\): \(B=0\) (minimum).
At the surface \((r=R)\): \(B\) is maximum.

Step 2: Verify statements
[A.] False (maximum is not at ends).
[B.] False.
[C.] False.
[D.] True.
[E.] False.
Final Answer: \[ \boxed{\text{(A) D Only}} \]