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QPages 384-386: Q44: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q44 Solution: A uniform magnetic field B exist in a region. An electron…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly apply the electrostatic force formula $F = kQq/r^2$ or assume a central potential, but in a magnetic field, the Lorentz force $F = evB$ is constant in magnitude and perpendicular to velocity, not dependent on $1/r^2$. Always derive the radius using the specific magnetic force balance $evB = mv^2/r$ rather than generic Bohr model formulas for hydrogen.

A uniform magnetic field B exist in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule for angular momentum, calculate a) the smallest possible radius of the electron b) the radius of the nth orbit and c) the minimum possible speed of the electron.

Step-by-Step Verified Solution

**Answer:** (a) r_min = sqrt(_/(eB)) (b) r_n = sqrt(n_/(eB)) (c) v_min = sqrt(eB_/m_). **Step-by-Step Explanation:** For electron in magnetic field, the quantization condition is mvr = n_. The radius is r = mv/(eB). Combining: r_n = sqrt(n_/(eB)). (a) n=1: r_min = sqrt(_/(eB)). (b) r_n = sqrt(n_/(eB)). (c) v_min = eB r_min / m = sqrt(eB_)/m [citation:3].

All Questions in this Chapter

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