KinexiaLEARN PHYSICS

Magnetic Force — Mass Spectrometer Ion (Worked Example)

Medium
Problem

In a mass spectrometer, an ion with charge 3.2 × 10⁻¹⁹ C travels at 2.0 × 10⁵ m/s perpendicular to a 0.80 T field. What magnetic force bends its path?

Given

  • q = 3.2 × 10⁻¹⁹ C

  • v = 2.0 × 10⁵ m/s

  • B = 0.80 T

Find

The magnetic force F.

Principle

F = qvB provides the centripetal force; measuring the bend radius reveals the ion's mass — how unknown substances are identified.

Formula

Solution

  1. Confirm geometry: the ion enters perpendicular to the field, so sin⁡θ=1\sin\theta = 1 and F=qvBF = qvB

  2. Substitute: F=(3.2×10−19)(2.0×105)(0.80)F = (3.2 \times 10^{-19})(2.0 \times 10^5)(0.80)

  3. Multiply: F=5.12×10−14 NF = 5.12 \times 10^{-14}\ \mathrm{N}

5.12 × 10⁻¹⁴ N

Unit check

C·m/s·T = N — correct.

What this means physically

5.12 × 10⁻¹⁴ N bends the ion into a measurable arc. Heavier ions bend less — the detector sorts molecules by mass from these tiny deflections.

Common mistake

Mixing up qvB with qE. Magnetic force needs velocity (qvB); electric force does not (qE) — different fields, different formulas.