Self Inductance of Solenoid – Rankers Physics

Self Induction: Practice Problem & Solution

Assertion (A): The self inductance of a solenoid can be increased by decreasing length if number of turns are fixed. Reason (R): Self inductance of a solenoid is directly proportional to current passing through it.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Self Induction. Understanding the underlying formula is key to arriving at the correct answer below:

Self inductance of a solenoid is given by \(L = \frac{\mu_0 N^2 A}{l}\). So, Assertion (A) is true as \(L\) is inversely proportional to \(l\). Self inductance \(L\) is a property of the coil's geometry and material, not dependent on current. So, Reason (R) is false. Thus, (A) is true but (R) is false.

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