Question

The magnitude of the magnetic field inside a long solenoid is increased by

• A. decreasing its radius
• B. decreasing the current through it
• C. increasing its area of cross-section
• D. introducing a medium of higher permeability
• E. decreasing the number of turns in it

Hint:

Inside a long solenoid, the magnetic field is uniform and constant. It is "dimension-independent" regarding radius and length, focusing only on density of turns and electrical input.

Answer 1

The Correct Option is D

Concept: The magnetic field (\(B\)) inside an ideal long solenoid is derived using Ampere's Circuital Law. \[ B = \mu n I \] Where:
• \(\mu = \mu_0 \mu_r\) is the permeability of the core material.
• \(n\) is the number of turns per unit length.
• \(I\) is the current.

Step 1: Analyze variable dependencies.
The formula \(B = \mu n I\) clearly shows that the field depends only on current, turn density, and the core material. It does not depend on the solenoid's radius or cross-sectional area. Thus, options (A) and (C) are incorrect.

Step 2: Evaluate the effect of permeability.
Decreasing current (B) or turns (E) would reduce \(B\). Introducing a ferromagnetic core increases \(\mu_r\), thereby increasing the total permeability \(\mu\) and the magnetic field strength significantly.