Two infinite current carrying wires having current I in opposite directions are shown below. Find the magnetic field (in S.I. units) at point P.

Correct Option: 10μ₀I/π (represented as 10μ₀l/π in the options)

Step-by-Step Explanation:

1. Identify the given parameters from the diagram:
The diagram shows two infinite parallel vertical wires carrying current $I$ in opposite directions.
The left wire carries current upwards, and the right wire carries current downwards.
Point $P$ is located between the two wires, at a perpendicular distance $r=10\text{cm}$ from both wires.

Convert the distance to S.I. units (meters):
$r=10\text{cm}=0.1\text{m}$

2. Formula for the magnetic field:
The magnitude of the magnetic field $B$ produced by an infinitely long straight wire carrying a current $I$ at a perpendicular distance $r$ is given by:
$B=\frac{{\mu }_{0}I}{2\pi r}$

3. Determine the direction of the magnetic field from each wire at point P:
- For the left wire: The current is flowing upwards. By applying the right-hand grip rule (pointing the right thumb in the direction of the current and curling the fingers around the wire), the magnetic field vector $B_1$ at point $P$ (which is to the right of the wire) points into the plane of the page.
- For the right wire: The current is flowing downwards. By applying the right-hand grip rule, the magnetic field vector $B_2$ at point $P$ (which is to the left of the wire) also points into the plane of the page.

Since both magnetic field vectors point in the same direction, the net magnetic field at point $P$ is the sum of their individual magnitudes:
$B_{\text{net}}=B_1+B_2$

4. Calculate the net magnetic field:
Substitute the values into the equations:
$B_1=\frac{{\mu }_{0}I}{2\pi \left(0.1\right)}=\frac{{\mu }_{0}I}{0.2\pi }=\frac{5{\mu }_{0}I}{\pi }$
Similarly, for the second wire:
$B_2=\frac{{\mu }_{0}I}{2\pi \left(0.1\right)}=\frac{5{\mu }_{0}I}{\pi }$
Adding them together to find the net magnetic field:
$B_{\text{net}}=\frac{5{\mu }_{0}I}{\pi }+\frac{5{\mu }_{0}I}{\pi }=\frac{10{\mu }_{0}I}{\pi }$

Thus, the magnetic field at point P in S.I. units is:
$B_{\text{net}}=\frac{10{\mu }_{0}I}{\pi }$