Question

Which expression gives the axial component \(dB_x\) from a loop element \(dl\)?

Options

• \(dB_x=\frac{\mu_0 I dl}{4\pi}\cdot\frac{x}{(x^2+R^2)^{3/2}}\)

• \(dB_x=\frac{\mu_0 I dl}{4\pi}\cdot\frac{1}{(x^2+R^2)^{1/2}}\)

• \(dB_x=\frac{\mu_0 I dl}{4\pi}\cdot\frac{R}{(x^2+R^2)^{3/2}}\)

• \(dB_x=\frac{\mu_0 I dl}{4\pi}\cdot\frac{R}{x^2+R^2}\)

Answer 1

The axial component is obtained by using the loop geometry with the Biot–Savart contribution. It is \(dB_x=\frac{\mu_0 I dl}{4\pi}\cdot\frac{R}{(x^2+R^2)^{3/2}}\).