Rotating Metallic Cylinder in Magnetic Field · RMPH 2016 #1

Physics · electromagnetism

Problem

A very long metallic cylinder (a perfect electric conductor), having the length LL and the radius RR, L≫RL \gg R rotates at constant angular speed ω\omega around its axis of symmetry. The cylinder is located in a homogeneous magnetic field whose induction B⃗\vec{B} is parallel to the axis of symmetry of the cylinder. The mass of electron is mm and his electric charge is −e-e. Let the dielectric permittivity of the material from which the cylinder is made be ε\varepsilon. 1.i. For a stationary situation determine the expression of the bulk density of electric charge ρ\rho into the cylinder at a distance rr from its axis of symmetry (0≤r≤R)(0 \leq r \leq R). Express the result as function of BB, ee, mm, ω\omega and ε\varepsilon. (1.00p) 1.ii. Determine the expression of angular velocity ω0\omega_0 so that the bulk charge density is zero at any point of the cylinder. Express the result as function of BB, ee and mm. (0.20p) 1.iii. Evaluate the possibility of the practical realization of a zero bulk charge density in any point of the metallic cylinder, when an experiment of the type described in question is carried out in the Earth's magnetic field in a place where the magnetic field induction is B=1.82×10−5TB = 1.82 \times 10^{-5} T. Briefly argue the answer. (0.30p)

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