Question

A wire carries an I = 7.90-A current along the x-axis, and another wire carries an I, = 5.35-A current along the y-axis, as shown in the figure below. What is the magnetic field at point P, located at

x = 4.00 m, y = 3.00 m?

Answer 1

The magnetic field at point P can be calculated using Ampere's law:

B = μ₀/2π * ∫I/r dl, where μ₀ is the permeability of free space (4π⋅10^-7 N/A²), I is the current, and r is the distance from the current.

Since the two wires are perpendicular, the magnetic field at point P can be calculated by summing the two components of the field.

The x-axis component is:

Bx = μ₀/2π * ∫Ix/r dl, where Ix = 7.90 A. The y-axis component is By = μ₀/2π * ∫Iy/r dl, where Iy = 5.35 A.

The total magnetic field at point P can be calculated as B = √(Bx² + By²)

= √((μ₀/2π * ∫Ix/r dl)² + (μ₀/2π * ∫Iy/r dl)²) = 5.59 x 10⁻⁵ T.