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Which of the following does NOT affect the magnetic field strength inside a current-carrying solenoid?
The number of turns per unit length
The magnitude of current flowing through it
The radius of the solenoid
The material of the core
The radius of the solenoid
The magnetic field strength inside an ideal infinite solenoid is determined solely by the number of turns per unit length, the current, and the permeability of the core material. The radius of the solenoid does not affect the interior magnetic field because the magnetic field lines are uniform and parallel inside the coil.
The magnetic field strength inside an ideal infinite solenoid is determined solely by the number of turns per unit length, the current, and the permeability of the core material. The radius of the solenoid does not affect the interior magnetic field because the magnetic field lines are uniform and parallel inside the coil.
Think of a solenoid like a tunnel; the strength of the magnetic field inside is like the traffic density within the tunnel, which depends on how many cars enter per meter and how fast they move, but not on the width of the tunnel itself.
Remember 'N-I-M': Number of turns, Intensity (current), Material (permeability). Radius is not in the NIM.
B=╬╝0тАЛnI тАФ Magnetic field strength of an ideal solenoid
n=LNтАЛ тАФ Number of turns per unit length
According to Ampere's Circuital Law, for an ideal solenoid, the magnetic field B is given by B=╬╝0тАЛnI. Here, n represents the number of turns per unit length (N/L). Since the field is assumed to be uniform within the solenoid, changing the cross-sectional area or radius does not change the flux density as long as the turns density remains constant.
The magnetic field inside an ideal solenoid is uniform.
The magnetic field outside an ideal solenoid is effectively zero.
The permeability of the core material (╬╝) replaces mu0тАЛ if the core is not air.
Electromagnets in industrial cranes
Inductors in electronic circuits
The formula B=╬╝0тАЛnI assumes an infinite solenoid where the length is much greater than the radius.
Option B (Current) is directly proportional: doubling current doubles the field.
Option A (Turns density) is directly proportional: increasing turns per meter increases the field.
Option D (Core material) is directly proportional: a soft iron core significantly increases the field compared to an air core due to high magnetic permeability.
C is correct тАФ The magnetic field strength inside an ideal solenoid is independent of its radius.
Always remember that 'Ideal' solenoid problems assume infinite length; if a question mentions 'short' or 'finite' solenoid, the geometry and radius may then become factors.