In a model of an electron orbiting in a uniform magnetic field B, magnetic flux through its orbit is quantized as Φ = nh/e, where n is an integer. For the lowest state n = 1, find the magnitude of its orbital magnetic dipole moment (m = electron mass).
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Question

In a model of an electron orbiting in a uniform magnetic field B, magnetic flux through its orbit is quantized as Φ = nh/e, where n is an integer. For the lowest state n = 1, find the magnitude of its orbital magnetic dipole moment (m = electron mass).

Options

G1 Physics · Accepted Answer

Step 1: Circular motion in B requires evB = mv²/r, giving v = eBr/m (use magnitudes). Step 2: The orbit carries current I = e/T = ev/(2πr). Step 3: Magnetic moment μ = Iπr² = evr/2. Step 4: Substitute v: μ = e²Br²/(2m). Step 5: Quantized flux Bπr² = nh/e implies Br² = nh/(πe). Step 6: Therefore μ = (e²/2m)[nh/(πe)] = neh/(2πm). Step 7: At n = 1, μ = eh/(2πm). Final answer: eh/(2πm), Option B.