Magnetic field at any point due to a short magnetic dipole derivation.

Figure $A$ and $B$ shown two long straight wires of circular cross-section ( $a$ and $b$ with $a<b$ ), carrying current $I$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $B$ varies with radius $r$ and can be represented as:

A current $I$ is flowing along an infinite, straight wire, in the positive $Z-$ direction and the same current is flowing along a similar parallel wire $5 \mathrm{m}$ apart, in the negative $Z-$ direction. A point $P$ is at a perpendicular distance $3 \mathrm{m}$ from the first wire and $4 \mathrm{m}$ from the second. What will be the magnitude of the magnetic field $B$ of $P$?

A long thin hollow metallic cylinder of radius $R$ has a current $i$ ampere. The magnetic induction $B$ away from the axis at a distance $\text{'}r\text{'}$ from the axis varies as shown in

A very long straight wire of radius $r$ carries current $I$. Intensity of magnetic field $B$ at a point lying at a perpendicular distance $a$ from the axis is $\propto$ _____ $(\text{where} a<r)$.

Two very long straight wires are set parallel to each other. Each carries a current $I$ in the same direction and the separation between them is $2r.$ The intensity of the magnetic field at point $P$ as shown in the figure is _________.