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What is the frequency of an electron (mass 9×10⁻³¹ kg and charge 1.6×10⁻¹⁹ C) moving at a speed of 3×10⁷ m s⁻¹ in a magnetic field of 4×10⁻⁴ T perpendicular to it?

Asked in GSEB Board August 2020 · Circular motion: radius, period and energy

• (1) 11.32 MHz
• (2) 1.7 MHz
• (3) 17 MHz
• (4) 1.132 MHz

Step-by-step solution

Why the other options are wrong

• (2) No single slip produces 1.7 MHz. Sanity check: f=(eB)/(2π m)=(1.6×10⁻¹⁹×4×10⁻⁴)/(2π×9×10⁻³¹)=1.132×10⁷ Hz.
• (3) 17 MHz has no route either — it is simply ten times the 1.7 MHz option, and both sit well away from (eB)/(2π m)=11.32 MHz.
• (4) 1.132 MHz is the right figure with the decimal point one place out: a lost power of ten in (eB)/(2π m).

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