Question

The self inductance of a long solenoid carrying current is independent of

• A. its length
• B. the current
• C. its cross-sectional area
• D. magnetic permeability of the core
• E. the number of turns

Hint:

Inductance depends on coil geometry, not on current flowing through it.

Answer 1

The Correct Option is B

Concept: Self-inductance of a solenoid
For a long solenoid: \[ L = \mu \frac{N^2 A}{\ell} \] where:
• $L$ = inductance
• $\mu$ = magnetic permeability of core
• $N$ = number of turns
• $A$ = cross-sectional area
• $\ell$ = length of solenoid ---

Step 1: Identify dependence
From the formula:
• $L \propto \mu$ → depends on material
• $L \propto N^2$ → depends on number of turns
• $L \propto A$ → depends on area
• $L \propto \frac{1}{\ell}$ → depends on length ---

Step 2: Check for current
Notice: \[ L \text{ does NOT contain current } I \] This means:
• Inductance is a property of geometry and material
• It does NOT depend on how much current is flowing ---

Step 3: Physical meaning

• Inductance tells how much emf is induced for a given rate of change of current
• It depends on structure, not the value of current --- Final Conclusion: \[ \boxed{\text{Inductance is independent of current}} \]