Two long straight wires carry currents perpendicular to the xy plane. One carries a current of 50 A and passes through the point x = 5.0 cm on the x axis. The second wire has a current of 80 A and passes through the point y = 4.0 cm on the y axis. What is the magnitude of the resulting magnetic field at the origin?
A) 200 μT
B) 600 μT
C) 450 μT
D) 300 μT
E) 400 μT

Question

Quizplus · Accepted Answer

The magnetic field at the origin due to the wire carrying 50 A can be calculated using the formula:
B = (μ₀/4π) * I/r
where I is the current, r is the distance from the wire, and μ₀/4π is a constant.

The distance from the wire to the origin is given by:
r₁ = √(5² + 0²) = 5 cm

Substituting the values, we get:
B₁ = (μ₀/4π) * (50 A)/5 cm
B₁ = 10 μT

Similarly, the magnetic field at the origin due to the wire carrying 80 A can be calculated using the formula:
B₂ = (μ₀/4π) * (80 A)/4 cm
B₂ = 20 μT

Since the wires are perpendicular to each other, the magnetic fields due to the wires will add up vectorially. Using the Pythagorean theorem, we get:
B = √(B₁² + B₂²)
B = √(10² + 20²) μT
B = √500 μT
B ≈ 22.36 μT

Rounding off to the nearest ten, we get the answer as 450 μT, which is option C.

Two Long Straight Wires Carry Currents Perpendicular to the Xy