Q.38 The magnetic field in the interior of a long current–carrying solenoid can be
increased by
(A) increasing the length of solenoid while keeping the number of turns per unit
length as constant
(B) increasing the number of turns per unit length
(C) increasing the current in the solenoid
(D) decreasing the length of solenoid while keeping the number of turns per unit
length as constant
The magnetic field inside a long current-carrying solenoid depends on specific parameters and can be increased by certain changes. The correct answer is options (B) and (C).
Solenoid Basics
A solenoid produces a uniform magnetic field B=μ0nI inside its interior for a long coil, where μ0 is the permeability of free space, n is turns per unit length, and I is current. This field remains constant along the axis, independent of position inside.
Option Analysis
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(A) Increasing length, constant n: Total turns N=nL rise proportionally with length L, but B depends only on n and I, not total N or L. Field stays unchanged.
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(B) Increasing turns per unit length: Directly raises n, so B increases linearly.
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(C) Increasing current: Directly raises I, so B increases linearly.
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(D) Decreasing length, constant n: Total turns drop as L decreases, but n fixed keeps B unchanged.
The magnetic field in the interior of a long current-carrying solenoid represents a fundamental concept in electromagnetism, crucial for exams like JEE or CSIR NET. Governed by B=μ0nI, this uniform field arises from Ampere’s law applied to the coil’s helical turns. Increasing the magnetic field in long current-carrying solenoid enhances applications like electromagnets and MRI machines.
Factors Affecting Field Strength
Field strength scales directly with turns per unit length (n=N/L) and current (I), remaining independent of total length or diameter for ideal long solenoids.
| Factor | Effect on B | Reason |
|---|---|---|
| Increase n | Increases | More turns per meter amplify field lines. |
| Increase I | Increases | Higher current boosts ampere-turns. |
| Increase L, constant n | No change | n unchanged. |
| Decrease L, constant n | No change | n fixed. |
Practical Implications
To increase magnetic field in long current-carrying solenoid, prioritize denser windings or higher amperage rather than altering length. Iron cores further amplify via permeability, though not in this query.
