NEETPhysicsElectromagnetic Induction
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When a given air-cored solenoid is physically stretched so that its length doubles (keeping the total number of turns and cross-sectional area constant), its self-inductance remains unchanged. Reason (R): The self-inductance of a long solenoid is directly proportional to the square of its turns per
Options
- ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
- BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
- CAssertion (A) is true and Reason (R) is false
- DAssertion (A) is false and Reason (R) is true
Correct answer
D. Assertion (A) is false and Reason (R) is true
Step-by-step solution
The self-inductance of a solenoid in terms of total turns N is given by L = ₀ N^2 A l . When the solenoid is stretched to double its length ( l' = 2l ) while keeping N and A constant, the new self-inductance becomes L' = ₀ N^2 A 2l = L 2 . Thus, the self-inductance becomes half of its original value, making Assertion (A) false. In terms of turns per unit length n ( n = N l ), the self-inductance is L = ₀ n^2 A l . This shows that self-inductance is directly proportional to the square of the turns per unit length (