An infinitely long wire carrying a current of 2 A is bent at a right angle as shown in the Figure. What is the magnetic field magnitude in Tesla a point P, 10 cm from the corner?

6.06810^6 T is wrong

Desribe the configuration of the bent wire

To find the magnetic field magnitude at point P, we can use Ampere's Law. Ampere's Law states that the integral of the magnetic field (B) dotted with the differential path length (dl) around a closed loop is equal to the product of the current enclosed by the loop (I_enc) and the permeability of free space (μ_0). Mathematically, it can be expressed as:

∮ B · dl = μ_0 * I_enc

In this case, the wire carrying the current is bent at a right angle, forming a corner. To calculate the magnetic field at point P, we can consider an imaginary circular loop centered at point P with a radius of 10 cm. By doing so, we enclose the current carrying wire within the loop.

To begin, let's determine the current enclosed by the loop. Since the wire is infinitely long, the current is constant along its entire length. However, only a portion of the current contributes to the magnetic field at point P. If we divide the wire into two sections, the current flowing through the vertical section of the wire bends towards point P, contributing to the magnetic field while the current along the horizontal section does not contribute since it is perpendicular to the line connecting point P.

Therefore, the current enclosed by the loop is equal to the current flowing through the vertical section, which is 2 A.

Next, we need to find the circumference of the circular loop centered around point P. The circumference of a circle can be calculated using the formula:

circumference = 2 * π * radius

Given that the radius is 10 cm, we can substitute it into the formula:

circumference = 2 * π * 0.1 m = 0.2π m

Now, we can calculate the magnetic field at point P using Ampere's Law. Rearranging the equation, we have:

B * circumference = μ_0 * I_enc

Substituting the values we know:

B * 0.2π m = (4π * 10^(-7) T·m/A) * 2 A

Simplifying:

B = (8π * 10^(-7) T·m/A) / (0.2π m)

The π cancels out, and we get:

B = (8 * 10^(-7) T·m/A) / (0.2 m)

B = 4 * 10^(-6) T

Therefore, the magnetic field at point P, 10 cm from the corner, is 4 * 10^(-6) Tesla (T).