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 a point P, 10 cm from the corner?
b=a•cos45 =0.1 •0.707 = 0.0707 m
B=2 (μ₀/4π)(I/b)∫cosφdφ {limits: (- π/4) (+π/2)}
=2(μ₀/4π)(I/b)(1+0.707)=
=2.1414 •(μ₀/4π) •2/0.0707=6.06•10⁻⁶T
To find the magnetic field at point P, we can use Ampere's Law. Ampere's Law states that the line integral of the magnetic field around a closed loop is equal to the product of the current passing through the loop and the permeability of free space (μ₀), which is a constant.
In this case, we can imagine a rectangular loop that encloses the wire segment, as shown in the figure. The loop has two straight sections and a curved section.
To calculate the magnetic field at point P, we need to calculate the contribution of the magnetic field due to each section of the loop.
1. Straight Section 1: The magnetic field due to the straight section of the wire can be calculated using the formula B = (μ₀ * I) / (2 * π * r₁), where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r₁ is the distance between the wire and point P. In this case, r₁ = 10 cm = 0.1 m.
2. Straight Section 2: The magnetic field due to the other straight section of the wire can also be calculated using the same formula as above. However, the distance between the wire and point P for this section is r₂ = 10 cm + the width of the wire. The width of the wire is not provided in the question, so we cannot calculate the exact value of r₂ unless it is given.
3. Curved Section: The magnetic field due to the curved section of the wire is constant and perpendicular to the plane of the loop. Therefore, the line integral of the magnetic field along this section is simply B * 2πr₃, where r₃ is the radius of the curved section. Again, the radius is not provided in the question, so we cannot calculate the exact value of the magnetic field for this section unless it is given.
To summarize, without knowing the width of the wire and the radius of the curved section, we cannot calculate the magnetic field at point P accurately.