In the Biot-Savart law,the direction of the magnetic field is determined by which of the following cross products in the expression $d\vec B = \frac{\mu_0}{4\pi} \frac{I d\vec l \times \vec r}{r^3}$?

What is the convention for an electric or magnetic field emerging out of the plane of the paper and going into the plane of the paper?

$A$ loop $ABCDA$,carrying current $I=12 \ A$,is placed in a plane,consists of two semi-circular segments of radius $R_1=6 \pi \ m$ and $R_2=4 \pi \ m$. The magnitude of the resultant magnetic field at center $O$ is $k \times 10^{-7} \ T$. The value of $k$ is . . . . . . . (Given $\mu_0=4 \pi \times 10^{-7} \ Tm \ A^{-1}$)

Which of the following is a vector quantity?

$A$ current of $0.1\, A$ circulates around a coil of $100$ turns and having a radius equal to $5\, cm$. The magnetic field set up at the centre of the coil is $({\mu _0} = 4\pi \times {10^{ - 7}}\,T\cdot m/A)$.

$A$ particle is moving with velocity $\overrightarrow{v} = \hat{i} + 3\hat{j}$ and it produces an electric field at a point given by $\overrightarrow{E} = 2\hat{k}$. It will produce a magnetic field at that point equal to (all quantities are in $SI$ units):