Question

How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth's (5.00 × 10-5 T)? Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)

a) 0.12 m
b) 0.24 m
c) 0.48 m
d) 0.60 m

Answer 1

To experience a magnetic field less than Earth's magnetic field, a person must be at least 0.12 meters away from a car's starter cable that carries a current of 150 A.

Step-by-step explanation:

The question asks about the distance required to be from a car's starter cable so that the magnetic field experienced is less than that of the Earth's magnetic field. Utilizing the formula for the magnetic field due to a long straight conductor, B = (μ₀)/(2π) * (I/r), where B is the magnetic field, μ₀ is the permeability of free space (4π x 10-7 T·m/A), I is the current, and r is the distance from the wire.

To find the distance where the magnetic field is equal to the Earth's magnetic field (5.00 x 10-5 T), this formula can be rearranged to solve for r: r = (μ₀)/(2π) * (I/B). Plugging in the values gives us r = (4π x 10-7 T·m/A)/(2π) * (150 A / 5.00 x 10-5 T), which calculates to r ≈ 0.12 m. Therefore, a person would need to be at least 0.12 m away from the starter cable to experience a field less than that of the Earth's.