$A$ thick current-carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B(r)$ due to the cable with the distance $r$ from the axis of the cable is represented by:

$A$ long solenoid carrying a current produces a magnetic field $B$ along its axis. If the current is doubled and the number of turns per cm is halved,the new value of the magnetic field is

Rank the value of $\oint \vec{B} \cdot d\vec{l}$ for the closed paths shown in the figure from the smallest to largest.

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current,the variation of magnetic field in the inside and outside region of the wire is :

What is the magnetic field inside a toroid having $0.1 \ m$ radius and $500$ turns when a current of $0.5 \ A$ is passed through it?

$A$ particle of mass $1 \times 10^{-27} \ kg$ and charge $1 \times 10^{-16} \ C$ enters a uniform magnetic field within a solenoid at a speed of $1000 \ m/s$. The velocity vector makes an angle of $60^{\circ}$ with the axis of the solenoid. The solenoid has $5000$ turns along its length $L$ and carries a current of $5 \ A$. The number of revolutions the particle makes along the helical path within the solenoid by the time it emerges from the solenoid's opposite end is: