The magnitude of the magnetic field inside a long solenoid is increased by

decreasing its radius

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decreasing the current through it

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increasing its area of cross-section

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introducing a medium of higher permeability

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decreasing the number of turns in it

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Solution

The correct option is D introducing a medium of higher permeability
By field along the axis of a solenoid
$B = μ_{0} n i$
where B = magnetic field .
$μ_{o}$ = permeability of free space
$n$ = the number of turns per unit length
$i$ = current
So, according to the formula, the magnitude of the magnetic field inside a long solenoid is increased by introducing a medium of higher permeability.

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The magnetic field inside a long solenoid having 50 turns $c m^{- 1}$ is increased from 2.5 $\times 10^{- 3}$ T to 2.5 T when an iron core of cross-sectional area 4 $c m^{2}$ is inserted into it. Find (a) the current in the solenoid, (b) the magnetization I of the core and (c) the Pole strength developed in the core.