$A$ wire carrying a current $i$ is placed in a uniform magnetic field $B$ in the form of the curve $y = a \sin \left( \frac{\pi x}{L} \right)$,where $0 \leq x \leq 2L$. The magnetic force on the wire is

Two parallel conductors, each $50 \ m$ long, separated by $0.2 \ m$, experience a force of $1 \ N$. If the current in the first conductor is twice that of the second conductor, what is the current in the second conductor (in $A$)? (Given: $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$)

$A$ wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\overrightarrow{B} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ T}$. The magnitude of the magnetic force acting on the wire is $..........IL$.

$A$ current $i = 2 \, A$ flows through a wire frame as shown in the figure. The frame is a combination of two equilateral triangles $ACD$ and $CDE$ with side length $1 \, m$. It is placed in a uniform magnetic field $B = 4 \, T$ acting perpendicular to the plane of the frame. The magnitude of the net magnetic force acting on the frame is.......$N$.

$A$ 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 $A$)? $(g=10 \ m \ s^{-2} \text{ and } \mu_0=4 \pi \times 10^{-7} \ T \ m \ A^{-1})$

$A, B$ and $C$ are three parallel conductors of equal lengths carrying currents $I, I$ and $2I$ respectively. The distance between $A$ and $B$ is $x$ and that between $B$ and $C$ is also $x$. $F_1$ is the force exerted by conductor $B$ on $A$. $F_2$ is the force exerted by conductor $C$ on $A$. The current $I$ in $A$ and $I$ in $B$ are in the same direction,and the current $2I$ in $C$ is in the opposite direction. Then: