$A$ long wire lies along the $X$-axis and carries a current of $40 \, A$ in the positive $x$-direction. $A$ second long wire is perpendicular to the $xy$-plane, passes through the point $(3.0 \, m) \hat{j}$, and carries a current along the positive $z$-direction. If the magnitude of the resultant magnetic field at the point $(2.0 \, m) \hat{j}$ is $R=5 \times 10^{-6} \, T$, then the current in the second wire is (Permeability of free space, $\mu_0=4 \pi \times 10^{-7} \, T \cdot m/A$) (in $A$)

Two long parallel wires carrying currents $8 \,A$ and $15 \,A$ in opposite directions are placed at a distance of $7 \,cm$ from each other. $A$ point $P$ is equidistant from both the wires such that the lines joining the point to the wires are perpendicular to each other. The magnitude of the magnetic field at point $P$ is $(\sqrt{2}=1.4)$ $(\mu_0=4 \pi \times 10^{-7} \,T \cdot m/A)$.

Two parallel wires in the plane of the paper are at a distance $X_0$ apart. $A$ point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\frac{X_0}{X_1}=3$, the value of $\frac{R_1}{R_2}$ is:

Write the formula for the force per unit length between two parallel,current-carrying conducting wires.

$A$ current carrying circular coil of radius $R$ produces magnetic fields $B_1$ and $B_2$ at an axial point $P$ at a distance $x$ from its centre and at a point $Q$ placed at its centre respectively. If $B_1 = \frac{B_2}{8}$,the value of $x$ is

The magnitude of the magnetic field at the center of an equilateral triangular loop of side $1 \ m$ which is carrying a current of $10 \ A$ is $.... \mu T$.