Explanation:

To find the magnitude of the magnetic field at point P, we can use the Biot-Savart law. According to this law, the magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.

Given:
- Two infinite planes carrying currents of linear densities k and -k.
- The current on one plane is directed into the paper, and on the other plane, it is directed out of the paper.

To simplify the problem, we can consider each plane as an infinite wire. The magnetic field at point P due to each wire can be determined separately and then added together.

Step 1: Magnetic Field due to the Plane with current density k:
- Consider a small section of the plane with width dx and length L.
- The current passing through this section is given by dI = k * dx.
- The magnetic field at point P due to this section can be calculated using the Biot-Savart law.
- The magnitude of the magnetic field at point P due to this section is given by dB = (μ0 * dI) / (2π * r), where μ0 is the permeability of free space and r is the distance between the section and point P.
- Since the plane is infinite, we need to integrate the contribution of the magnetic field from all sections along the plane.
- The total magnetic field at point P due to the plane with current density k is given by integrating dB over the entire length of the plane.

Step 2: Magnetic Field due to the Plane with current density -k:
- Similar to the previous step, we consider a small section of the plane with width dx and length L.
- The current passing through this section is given by dI = -k * dx.
- The magnetic field at point P due to this section is given by dB = (μ0 * dI) / (2π * r).
- Again, we need to integrate the contribution of the magnetic field from all sections along the plane.
- The total magnetic field at point P due to the plane with current density -k is given by integrating dB over the entire length of the plane.

Step 3: Total Magnetic Field at point P:
- To calculate the total magnetic field at point P, we add the contributions from both planes.
- Since one plane has current density k and the other has -k, the magnetic fields due to these planes will have opposite directions.
- Therefore, we subtract the magnetic field due to the plane with current density -k from the magnetic field due to the plane with current density k to get the total magnetic field at point P.

The magnitude of the magnetic field at point P can be calculated using the formula: B = |Bk - B(-k)|.

Note: The exact values of the linear densities k and -k, as well as the distances and dimensions of the planes, are not specified in the question. Therefore, the final answer will depend on these values.