An electron of mass m is accelerated through a potential difference V and then enters a magnetic field of induction B perpendicular to the field lines. What is the radius of the resulting circular path?

sqrt(2eV/m)
sqrt(2Vm / (eB²))
sqrt(2Vm / e) / B
sqrt(2Vm / (e² * B))

Correct answer: sqrt(2Vm / (eB²))

Solution

From eV = (1/2)mv²: v = sqrt(2eV/m). Radius r = mv/(eB) = m * sqrt(2eV/m) / (eB) = sqrt(2m²*eV/m) / (eB) = sqrt(2meV) / (eB) = sqrt(2mV/e) / B. This equals sqrt(2Vm/(eB²)).

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