$A$ long solenoid is fabricated by closely winding a wire of radius $0.5 \, mm$ over a cylindrical frame so that the successive turns nearly touch each other. What is the magnetic field at the centre of the solenoid if it carries a current of $5 \, A$?

Assertion : If the current in a solenoid is reversed in direction while keeping the same magnitude,the magnetic field energy stored in the solenoid decreases.
Reason : Magnetic field energy density is proportional to the square of the current.

$A$ magnetic field of $100 \;G$ $(1 \;G = 10^{-4} \;T)$ is required which is uniform in a region of linear dimension about $10 \;cm$ and area of cross-section about $10^{-3} \;m^2$. The maximum current-carrying capacity of a given coil of wire is $15 \;A$ and the number of turns per unit length that can be wound round a core is at most $1000 \;turns \;m^{-1}$. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

Consider two solenoids $X$ and $Y$ such that the area and length of $Y$ are twice that of $X$ respectively and the magnetic energy stored in both the solenoids is same,then the ratio of magnitude of magnetic fields of the two solenoids $\frac{|B_X|}{|B_Y|}$ is

Choose the wrong statement to complete: An ideal solenoid has

$A$ solenoid of length $50 \,cm$ having $100$ turns carries a current of $2.5 \,A$. The magnetic field at one end of the solenoid is