Two concentric loops $A$ and $B$ of same radius $R = 2 \pi \,cm = 2 \pi \times 10^{-2} \,m$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are $I_A = 3 \,A$ and $I_B = 4 \,A$ respectively, then the net magnetic field at their common centre is:

$A$ charged particle of mass $m$ and charge $q$ moving under the influence of a uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$ follows a trajectory from point $P$ to $Q$ as shown in the figure. The velocities at $P$ and $Q$ are respectively $v\hat{i}$ and $-2v\hat{j}$. Which of the following statements $(A, B, C, D)$ are correct? (Trajectory shown is schematic and not to scale)
$(A)$ $E = \frac{3}{4}\left(\frac{mv^{2}}{qa}\right)$
$(B)$ Rate of work done by the electric field at $P$ is $\frac{3}{4}\left(\frac{mv^{3}}{a}\right)$
$(C)$ Rate of work done by both the fields at $Q$ is zero
$(D)$ The difference between the magnitude of angular momentum of the particle at $P$ and $Q$ is $2mav$.

Which of the following statements is correct?

Two straight long conductors $AOB$ and $COD$ are perpendicular to each other and carry currents $i_1$ and $i_2$. The magnitude of the magnetic induction at a point $P$ at a distance $a$ from the point $O$ in a direction perpendicular to the plane $ACBD$ is

Two infinite line-charges parallel to each other are moving with a constant velocity $v$ in the same direction as shown in the figure. The separation between two line-charges is $d$. The magnetic attraction balances the electric repulsion when,[$c$ = speed of light in free space]

One of the two small circular coils (neither having any self-inductance) is suspended with a $V$-shaped copper wire,with its plane horizontal. The other coil is placed just below the first one with its plane horizontal. Both coils are connected in series with a $dc$ supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect?