The correct option is 10μ₀l/π.

Step-by-step Explanation:

From the provided image, we can identify two infinite straight current-carrying wires positioned vertically. The left wire has a current pointing upwards (represented by the upward arrow), and the right wire has an equal current pointing downwards (represented by the downward arrow). Let the current in each wire be represented by the symbol l. The point P is located in the middle, at a distance of 10 cm from both the left and right wires.

First, let us convert the distance from centimeters to meters (SI units):

$r=10\text{cm}=0.1\text{m}$

According to Ampere's Law, the magnetic field B due to a long, straight, infinite wire carrying current l at a distance r is given by the formula:

$B=\frac{{\mu }_{0}l}{2\pi r}$

Now, let us determine the direction of the magnetic field at point P due to each wire using the right-hand rule:

1. For the left wire (current pointing upwards): If we point the thumb of our right hand in the direction of the current (upwards) and curl our fingers, at the location of point P (which is to the right of the wire), our fingers point into the plane of the page. Thus, the magnetic field $B_1$ is directed into the page.

2. For the right wire (current pointing downwards): If we point the thumb of our right hand in the direction of the current (downwards) and curl our fingers, at the location of point P (which is to the left of the wire), our fingers also point into the plane of the page. Thus, the magnetic field $B_2$ is also directed into the page.

Since both magnetic fields point in the same direction (into the page), the net magnetic field $B_{\text{net}}$ at point P is the sum of the magnitudes of the individual magnetic fields:

$B_{\text{net}}=B_1+B_2$

Substituting the expression for the magnetic field of each wire:

$B_{\text{net}}=\frac{{\mu }_{0}l}{2\pi r}+\frac{{\mu }_{0}l}{2\pi r}=\frac{{\mu }_{0}l}{\pi r}$

Substitute the value of distance $r=0.1\text{m}$ into the equation:

$B_{\text{net}}=\frac{{\mu }_{0}l}{\pi \left(0.1\right)}=\frac{10{\mu }_{0}l}{\pi }$