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The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as  
  • a)
    l and A  increase  
  • b)
    l decreases and A increases  
  • c)
    l increa ses and A decreases
  • d)
    both l and A decrease 
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The self inductance L of a solenoid of length l and area of cross-sect...
Key concept: The self inductance L of a solenoid depends on various factor like geometry and magnetic permeability of the core material.
L = μr μn2 Al
where, n = N/l (no. of turns per unit length)
1.   No. of turns: Larger the number of turns in solenoid, larger is its self inductance.
2.  Area of cross section: Larger the area of cross section of the solenoid, larger is its self inductance.
3.  Permeability of the core material. The self inductance of a solenoid increases μr times if it is wound over an iron core of relative permeability μr.
The long solenoid of cross-sectional area A and length l, having A turns, filled inside of the solenoid with a material of relative permeability (e.g., soft iron, which has a high value of relative permeability) then its self inductance is L = μrμ0 N2 A/l
So, the self inductance L of a solenoid increases as l decreases and A increases because L is directly proportional to area and inversely proportional to length.
Important point: The self and mutual inductance of capacitance and resistance depend on the geometry of the devices as well as permittivity/ permeability of the medium.  
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The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as a)l and A increase b)l decreases and A increases c)l increa ses and A decreasesd)both l and A decreaseCorrect answer is option 'B'. Can you explain this answer?
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