$A$ wire carrying a steady current $I$ is kept in the $x$-$y$ plane along the curve $y=A \sin \left(\frac{2 \pi}{\lambda} x\right)$. $A$ magnetic field $B$ exists in the $z$-direction. The magnitude of the magnetic force on the portion of the wire between $x=0$ and $x=\lambda$ is

$A$ horizontal wire carries $160 \ A$ current. Below it, another wire with a linear mass density of $10 \ g \ m^{-1}$ is kept at a distance of $4 \ cm$. If the lower wire hangs in the air, what is the current in this wire when the direction of current in both wires is the same (in $A$)? $(g=10 \ m \ s^{-2} \text{ and } \mu_0=4 \pi \times 10^{-7} \ T \ m \ A^{-1})$

The horizontal component of the earth's magnetic field at a certain place is $3.0 \times 10^{-5} \; T$ and the direction of the field is from the geographic south to the geographic north. $A$ very long straight conductor is carrying a steady current of $1 \; A$. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is $(a)$ east to west; $(b)$ south to north?

$A$ rectangular loop of sides $25 \text{ cm}$ and $10 \text{ cm}$ carrying a current of $10 \text{ A}$ is placed with its longer side parallel to a long straight conductor $10 \text{ cm}$ apart carrying a current of $25 \text{ A}$. The net force on the loop is

Find the force per unit length at point $P$. The current in the wire is $5 \, A$ and the distance between the parallel segments is $10 \, cm$.

Two long conductors separated by a distance $d$ carry currents $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now,the current in one of them is increased to $2$ times and its direction is reversed. The distance between them is also increased to $3d$. The new value of force between them is: