Question

Which expression gives the scalar (magnitude) form of the Biot–Savart law for the magnetic field contribution dB of a current element?

Options

• \[dB = \frac{\mu_0}{4\pi}\frac{I\,dl\,\cos\theta}{r^2}\]

• \[dB = \frac{\mu_0}{4\pi}\frac{I\,dl\,\sin\theta}{r^2}\]

• \[dB = \frac{\mu_0}{4\pi}\frac{I\,dl\,\sin\theta}{r^3}\]

• \[dB = \frac{\mu_0}{4\pi}\frac{I\,dl\,\sin\theta}{r}\]

Answer 1

Combining the four proportionalities (dB ∝ I, dB ∝ dl, dB ∝ sinθ, dB ∝ 1/r²) gives dB = (μ₀/4π)(Idl sinθ)/r². The constant μ₀/4π is needed to make the units work out correctly in the SI system.