Tag: field due to a current carrying conductor

because angle between line and distance becomes zero.
$\therefore\overrightarrow{l}\times\widehat{r}$  becomes zero.

Answer is D.

The magnitude and direction of F depend on the velocity of the particle and on the magnitude and direction of the magnetic field B.
When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero.
When the particles velocity vector makes any angle with the magneticfield, the magnetic force acts in a direction perpendicular to both v and B; that is, F is perpendicular to the plane formed by v and B.
The magnitude of the magnetic force is
$F=qvBsin\theta $
where $\theta $ is the smaller angle between v and B. From this expression, we see that F is zero when v is parallel or antiparallel to B or 180) and maximum when v is perpendicular to B.
In this case, as the proton moves parallel to the magnetic field, the force is zero.

Magnetic field due to large wire is 

The physical constant $μ _0$ commonly called the vacuum permeability, permeability of free space, ... In the reference medium of classical vacuum, μ0 has an exact defined value: .... The value of $μ _0$ was chosen such that the rmks unit of current is equal in size to the ampere in the emu system: μ0 is defined to be $4π × 10^{−7} H/m.$

The Biot Savart law is used for computing the resultant magnetic field B at position r generated by a steady current I.  According to it $B=\frac {\mu _0 I } {4\pi} \int \frac {I\vec{dl} \times \vec{r}} { r^3}$.
So magnetic field at a distance r and lying on the plane perpendicular ($\pi /2$)to the element of conductor is maximum .