Two long straight parallel wires $A$ and $B$ separated by $5 \ m$ carry currents $2 \ A$ and $6 \ A$ respectively in the same direction. The resultant magnetic field due to the two wires at a point $P$ at a distance of $2 \ m$ from wire $A$ in between the two wires is:

$A$ dielectric circular disc of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$,the magnetic field at the center of the disc is:

$A$ circular coil $A$ has a radius $R$ and the current flowing through it is $I$. Another circular coil $B$ has a radius $2R$ and the current flowing through it is $2I$. The ratio of the magnetic fields at the centre of the circular coils $(B_A : B_B)$ is: (in $:1$)

Match List-$I$ with List-$II$. Choose the correct answer from the options given below:

$A$ semi-circular arc of radius $r$ and a straight wire along the diameter,both are carrying the same current $i$. Find out the magnetic force per unit length on the small element $P$,which is at the center of the diameter.

To produce a uniform magnetic field directed parallel to a diameter of a cylindrical region,one can use the saddle coils illustrated in the figure. The loops are wrapped over a somewhat flattened tube. Assume the straight sections of wire are very long. The end view of the tube shows how the windings are applied. The overall current distribution is the superposition of two overlapping circular cylinders of uniformly distributed current,one toward you and one away from you. The current density $J$ is the same for each cylinder. The position of the axis of one cylinder is described by a position vector $\vec{a}$ relative to the other cylinder. The magnetic field inside the hollow tube is: