Question

Which set of proportionalities correctly describes how the magnitude dB of the magnetic field contribution depends on the current I, the element length dl, the angle θ, and the distance r?

Options

• \[dB \propto I, \quad dB \propto dl^2, \quad dB \propto \tan\theta, \quad dB \propto \frac{1}{r^3}\]

• \[dB \propto I, \quad dB \propto dl, \quad dB \propto \cos\theta, \quad dB \propto \frac{1}{r^2}\]

• \[dB \propto I^2, \quad dB \propto dl, \quad dB \propto \sin\theta, \quad dB \propto \frac{1}{r}\]

• \[dB \propto I, \quad dB \propto dl, \quad dB \propto \sin\theta, \quad dB \propto \frac{1}{r^2}\]

Answer 1

Experiments show that dB is proportional to the current I, the element length dl, and sinθ, and inversely proportional to the square of the distance r. The 1/r² dependence is the same inverse-square pattern as gravity and electric fields.