Magnetic induction is a

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$, making an angle $\theta$ with the current element, then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

Which of the following statements is false for Helmholtz coils?

Write the formula for the magnetic field due to a circular current-carrying loop having $N$ turns and $R$ radius at a point on the axis of the loop at a distance $x$ from the center.

$A$ particle carrying a charge equal to $100$ times the charge on an electron is rotating one rotation per second in a circular path of radius $0.8 \ m$. The value of magnetic field produced at the centre will be $(\mu_0 = \text{permeability of vacuum})$

Two identical long parallel wires carry currents $I_1$ and $I_2$ such that $I_1 > I_2$. When the currents are in the same direction,the magnetic field at a point midway between the wires is $8 \times 10^{-6} \ T$. If the direction of $I_2$ is reversed,the field becomes $3.2 \times 10^{-5} \ T$. The ratio of $I_2$ to $I_1$ is