Question 18 of 276
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 ends of the conductor and minimum at the midpoint
B. maximum at the axis of the conductor
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 :
Show answer and solution
Answer: (B) D Only
For a long cylindrical conductor with uniform current distribution, apply Ampere's law to find the magnetic field.
At distance from the axis (inside the conductor, ): (proportional to )
At the axis (): (minimum)
At the surface (): (maximum)
Analyzing the statements:
A. Maximum at ends and minimum at midpoint - FALSE. This describes behavior along the axis, but the magnetic field depends on radial distance, not axial position.
B. Maximum at the axis of the conductor - FALSE. The field is zero at the axis.
C. Minimum at the surface of the conductor - FALSE. The field is maximum at the surface.
D. Minimum at the axis of the conductor - TRUE. The field is zero at , making it the minimum.
E. Same at all points in the cross-section - FALSE. The field varies from 0 at the axis to maximum at the surface.
Only D is correct.
At distance from the axis (inside the conductor, ): (proportional to )
At the axis (): (minimum)
At the surface (): (maximum)
Analyzing the statements:
A. Maximum at ends and minimum at midpoint - FALSE. This describes behavior along the axis, but the magnetic field depends on radial distance, not axial position.
B. Maximum at the axis of the conductor - FALSE. The field is zero at the axis.
C. Minimum at the surface of the conductor - FALSE. The field is maximum at the surface.
D. Minimum at the axis of the conductor - TRUE. The field is zero at , making it the minimum.
E. Same at all points in the cross-section - FALSE. The field varies from 0 at the axis to maximum at the surface.
Only D is correct.
