$A$ charged particle moves with constant velocity in a region where no effect of gravity is felt, but an electrostatic field $\vec{E}$ together with a magnetic field $\vec{B}$ may be present. Which of the following cases are possible?

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:

$A$ particle of charge $q$ and mass $m$ is moving along the $x$-axis with a velocity $v$ and enters a region of electric field $E$ and magnetic field $B$ as shown in the figures below. For which figure may the net force on the charge be zero?

Two parallel long wires carry currents $i_1$ and $i_2$ with $i_1 > i_2$. When the currents are in the same direction,the magnetic field midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,it becomes $40 \, \mu T$. The ratio $i_1/i_2$ is

The magnetic field at the centre of a circular coil of radius $r$ is $\pi$ times that due to a long straight wire at a distance $r$ from it,for equal currents. Figure shows three cases: in all cases,the circular part has radius $r$ and straight ones are infinitely long. For the same current,the $B$ field at the centre $P$ in cases $1$,$2$,and $3$ have the ratio:

$A$ very long wire $ABDMNDC$ is shown in the figure carrying current $I$. $AB$ and $BC$ parts are straight,long,and at a right angle. At $D$,the wire forms a circular turn $DMND$ of radius $R$. $AB$ and $BC$ parts are tangential to the circular turn at $N$ and $D$. The magnetic field at the centre of the circle is