KinexiaLEARN PHYSICS

Magnetic Force — Aurora Electron (Worked Example)

Medium
Problem

A solar-wind electron streams at 5.0 × 10⁶ m/s perpendicular to Earth's magnetic field (5.0 × 10⁻⁵ T) near the poles. What magnetic force deflects it?

Given

  • q = 1.602 × 10⁻¹⁹ C

  • v = 5.0 × 10⁶ m/s

  • B = 5.0 × 10⁻⁵ T

Find

The magnetic force F.

Principle

Earth's field steers charged particles via F = qvB — the mechanism behind auroras.

Formula

Solution

  1. Confirm perpendicular motion: the electron's velocity is perpendicular to Earth's field, so F=qvBF = qvB applies fully

  2. Substitute: F=(1.602×10−19)(5.0×106)(5.0×10−5)F = (1.602 \times 10^{-19})(5.0 \times 10^6)(5.0 \times 10^{-5})

  3. Multiply: F=4.01×10−17 NF = 4.01 \times 10^{-17}\ \mathrm{N}

4.01 × 10⁻¹⁷ N

Unit check

C·m/s·T = N — correct.

What this means physically

4.01 × 10⁻¹⁷ N — minuscule, but it curves the electron's path over thousands of kilometres, funnelling it into the polar atmosphere where it lights up the aurora.

Common mistake

Using Earth's surface field (∼5×10⁻⁵ T is right) but wrong direction assumptions. Magnitude first with F = qvB; direction needs the right-hand rule separately.