$A$ current-carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of the solenoid. If $g$ is the acceleration due to gravity, then the acceleration $(a)$ of the charged particle will satisfy:

The free space inside a current-carrying toroid is filled with a material of magnetic susceptibility $2 \times 10^{-2}$. The percentage increase in the value of the magnetic field inside the toroid will be $.....\%$.

The magnetic field inside a current-carrying toroidal solenoid is $0.2 \ mT$. What is the magnetic field inside the toroid if the current is tripled (in $mT$)?

$A$ current $I$ flows along the length of an infinitely long,straight and thin-walled pipe. Then

$A$ solenoid $60 \;cm$ long and of radius $4.0\; cm$ has $3$ layers of windings of $300$ turns each. $A$ $2.0 \;cm$ long wire of mass $2.5\; g$ lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of $6.0\; A$ in the wire. What value of current (in $A$) in the windings of the solenoid can support the weight of the wire? $(g=9.8\; m \,s ^{-2})$

$A$ long cylindrical conductor with a large cross-section carries an electric current distributed uniformly over its cross-section. The magnetic field due to this current is: