What is the magnetic dipole moment of an electron revolving in a circular orbit of radius 'r' with a uniform speed 'v'? MCQ with Answer and Explanation
What is the magnetic dipole moment of an electron revolving in a circular orbit of radius 'r' with a uniform speed 'v'?
A. evr
B. evr / 2
C. e / (vr)
D. 2evr
Answer: Option B
Solution (By JKExamLibrary)
Magnetic dipole moment M = Current(I) * Area(A). Current is charge/time: I = e / T. Time period T = 2pir / v. So I = ev / (2pir). The area of the circular orbit is A = pir^2. Therefore, M = [ev / (2pir)] * [pir^2] = evr / 2. This is a standard derivation in modern physics.
Explanation:
Resistance R = ρL/A, where ρ is resistivity (material property). New length L' = 2L, new area A' = A/2. Thus R' = ρ(2L)/(A/2) = ρ·2L·2/A = 4(ρL/A) = 4R. Resistance scales directly with length and inversely with area. Memory tip: 'Double length ⇒ double R; halve area ⇒ double R; combined ⇒ 4×'. This proportional reasoning problem is frequent in electricity sections of competitive exams. Always verify if resistivity changes (it doesn't here, same material).
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