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# A long solenoid of length L has a mean diameter D. It has n layers of windings of N turns each. If it carries a current I, the magnetic field at its centre will be:A. Proportional to D.B. Inversely proportional to D.C. Independent of D.D. Proportional to L.

Last updated date: 14th Jun 2024
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Hint:Recall the expression for the magnetic field at the centre of the solenoid. The magnetic field is proportional to the number of turns per unit length of the solenoid. Check the dependence of the magnetic field on the diameter of the solenoid.

$B = {\mu _0}nI$
Here, B is the magnetic field, n is the number of turns per unit length, ${\mu _0}$ is the permeability of the free space and I is the current.
$B = \dfrac{{{\mu _0}NI}}{L}$
Note: In the formula, $B = {\mu _0}nI$, n is the number of turns per unit length and not the number of turns. Therefore, the magnetic field at the centre of the solenoid also depends on the length of the solenoid. Note that the solenoid must be very long so that the formula $B = {\mu _0}nI$ remains valid.