At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of Earth's magnetic field of about 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A) A)1.0 mm B)1.0 cm C)2.0 cm D)3.0 cm E)4.0 cm

Question

Quizplus · Accepted Answer

The magnetic field at a distance r from a long straight wire carrying a current I is given by:

B = (μ0/2π) × (I/r)

where μ0 = 4π × 10^-7 T∙m/A is the permeability of free space.

We need to find the distance at which the magnetic field B from the wire is equal to the Earth's magnetic field strength of 5.0 × 10^-5 T.

Equating the two magnetic fields, we get:

(μ0/2π) × (5.0 A/r) = 5.0 × 10^-5 T

Solving for r, we get:

r = (μ0/2π) × (5.0 A/5.0 × 10^-5 T) ≈ 0.02 m = 2.0 cm

Therefore, the answer is C) 2.0 cm.

At What Distance from a Long Straight Wire Carrying a Current