The magnetic field at point $P$ in the given figure, due to a current $I$ flowing through a cylindrical conductor of radius $R$, is:

Two wires carrying currents of $5 \ A$ and $2 \ A$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3 \ A$ is situated outside the loop. The value of $\oint \overrightarrow{B} \cdot d\overrightarrow{l}$ around the loop is ($\mu_0 = \text{permeability of free space}$,$d\overrightarrow{l}$ is the length element of the Amperian loop).

$A$ solenoid has a turn density of $5000 \, \text{turns/m}$ and a cross-sectional area of $10 \, \text{cm}^2$. If a current of $1 \, \text{A}$ flows through it and the core material has a relative permeability of $1000$, find the energy per unit length of the solenoid in $\text{J/m}$.

What is the magnetic field at point $P$ in the given figure?

$A$ 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

$A$ straight wire of diameter $0.4 \,mm$ carrying a current of $2 \,A$ is replaced by another wire of $0.8 \,mm$ diameter carrying the same current. The magnetic field at distance $R$ from both the wires is $B_1$ and $B_2$ respectively. The relation between $B_1$ and $B_2$ is