Magnetic Effects of Current Questions

A long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross section. The ratio of the magnetic field at distance $a/2$ and $2a$ from the axis is:

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

A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$ with a velocity $\vec{v}$ perpendicular to both $\vec{E}$ and $\vec{B}$, and comes out without any change in magnitude or direction of $\vec{v}$. Then:

A charged particle moves through a magnetic field perpendicular to its direction. Then:

Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current $I_1$ and $COD$ carries a current $I_2$. The magnetic field on a point lying at a distance $d$ from $O$, in a direction perpendicular to the plane of the wires, will be given by: