KinexiaLEARN PHYSICS

Magnetic Force — CRT Electron Beam (Worked Example)

Easy
Problem

An old CRT television steers its electron beam with a 1.0 mT magnetic field. An electron moving at 2.0 × 10⁷ m/s enters perpendicular to the field. What force steers it? (e = 1.602 × 10⁻¹⁹ C)

Given

  • q = 1.602 × 10⁻¹⁹ C

  • v = 2.0 × 10⁷ m/s

  • B = 1.0 mT = 1.0 × 10⁻³ T

Find

The magnetic force F.

Principle

F = qvB steers the beam — scanning it across the screen 15,000+ times per second to paint the picture.

Formula

Solution

  1. Convert: B=1.0×10−3 TB = 1.0 \times 10^{-3}\ \mathrm{T}

  2. Substitute: F=(1.602×10−19)(2.0×107)(1.0×10−3)F = (1.602 \times 10^{-19})(2.0 \times 10^7)(1.0 \times 10^{-3})

  3. Multiply: F=3.20×10−15 NF = 3.20 \times 10^{-15}\ \mathrm{N}

3.20 × 10⁻¹⁵ N

Unit check

C·m/s·T = N — correct.

What this means physically

3.20 × 10⁻¹⁵ N — enough to deflect the near-massless electron across the screen in microseconds. Modern flat panels replaced this with liquid crystals, but the physics demo is a classic.

Common mistake

Leaving B in millitesla. Convert mT → T (×10⁻³) before multiplying, or the force comes out 1000× too big.