Two identical long parallel wires carry currents $I_1$ and $I_2$ such that $I_1 > I_2$. When the currents are in the same direction,the magnetic field at a point midway between the wires is $6 \times 10^{-6} \ T$. If the direction of $I_2$ is reversed,the field becomes $3 \times 10^{-5} \ T$. The ratio $\left(\frac{I_1}{I_2}\right)$ is-

$A$ long solenoid with $1000 \, \text{turns/m}$ has a core material with relative permeability $500$ and volume $10^{3} \, \text{cm}^{3}$. If the core material is replaced by another material having relative permeability of $750$ with the same volume, maintaining the same current of $0.75 \, \text{A}$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right)$. Find the value of $x$.

The magnetic field at the center of a current-carrying loop of radius $0.1 \ m$ is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the center of the loop is: (in $m$)

Which of the following graphs shows the variation of magnetic induction $B$ with distance $r$ from a long straight wire carrying current?

An element $\overrightarrow{\Delta \ell} = \Delta x \hat{i}$ is placed at the origin and carries a current of $10 \ A$. Find the magnitude of the magnetic field on the $Y$-axis at a distance of $0.5 \ m$,given $\Delta x = 1 \ cm$. (Use $\frac{\mu_0}{4 \pi} = 10^{-7} \ T \cdot m/A$)

Shown in the figure is a conductor carrying a current $I$. The magnetic field intensity at the point $O$ (common centre of all the three arcs) is