$A$ circular coil of wire consisting of $100$ turns each of radius $9 \ cm$ carries a current of $0.4 \ A$. The magnitude of the magnetic field at the centre of the coil is $[\mu_0 = 12.56 \times 10^{-7} \text{ SI Units}]$.

The correct Biot-Savart law in vector form is

The unit vectors $\hat{i}, \hat{j},$ and $\hat{k}$ are as shown below. What will be the magnetic field at $O$ in the following figure?

Give similarity between Biot-Savart law and electrostatic law of Coulomb.

The magnetic field due to a current-carrying circular loop of radius $3 \ cm$ at a point on the axis at a distance of $4 \ cm$ from the centre is $54 \ \mu T$. What will be its value at the centre of the loop? (in $\mu T$)

$A$ single current-carrying loop of wire with current $I$ flowing in an anticlockwise direction when seen from the $+ve\;z$ direction,lying in the $xy$ plane,is shown in the figure. The plot of the $\hat{j}$ component of the magnetic field $(B_y)$ at a distance $a$ (less than the radius of the coil) on the $yz$ plane versus the $z$ coordinate looks like: