An electron moves in a circular orbit at uniform speed v. The magnetic field produced by its motion at the centre is B. What is the radius r of the orbit proportional to?
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An electron moves in a circular orbit at uniform speed v. The magnetic field produced by its motion at the centre is B. What is the radius r of the orbit proportional to?

G1 Physics · Accepted Answer

Step 1: An orbiting electron of charge magnitude e constitutes current I = e/T = ev/(2πr). Step 2: Magnetic field at the centre of circular current is B = μ₀I/(2r). Step 3: B = μ₀ev/(4πr²) ⇒ r² = μ₀ev/(4πB). Step 4: Keeping physical constants fixed, r ∝ √(v/B). Final answer: (C) √(v/B).