A particle of charge q in a cylindrical magnetron moves in a uniform magnetic field B = Bzˆ and an electric field, directed radially outward or inward from a central wire along the z-axis, E = a ρ ρˆ. The constants a and B may be either positive or negative. (a) Set up the equations of motion in cylindrical coordinates. (b) Show that the quantity mρ2φ˙ + qBp^2/2 = K is a constant of the motion. (c) Using this result, give a qualitative discussion, based on the energy integral, of the types of motion that can occur. Consider all cases, including all values of a, B, K, and E. (d) Under what conditions can circular motion about the axis occur? (e) What is the frequency of small radial oscillations about this circular motion

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A particle of charge q in a cylindrical magnetron moves in a uniform magnetic field B = Bzˆ and an electric field, directed radially outward or inward from a central wire along the z-axis, E = a ρ ρˆ. The constants a and B may be either positive or negative. (a) Set up the equations of motion in cylindrical coordinates. (b) Show that the quantity mρ2φ˙ + qBp^2/2 = K is a constant of the motion. (c) Using this result, give a qualitative discussion, based on the energy integral, of the types of motion that can occur. Consider all cases, including all values of a, B, K, and E. (d) Under what conditions can circular motion about the axis occur? (e) What is the frequency of small radial oscillations about this circular motion

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Science leeo 9 months 2024-12-10T20:08:02+05:00 2024-12-10T20:08:02+05:00 1 Answer 14 views Beginner

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