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According to Yukawa’s theory of nuclear forces, the attractive force between a neutron and a proton has the potential V (r) = −Ke^(−αr)/r, K, α > 0 (a) Find the force, and compare it with an inverse square law of force. (b) Discuss the types of motion which can occur if a particle of mass m moves under such a force. (c) Discuss how the motions will be expected to differ from the corresponding types of motion for an inverse square law of force. (d) Find L and E for motion in a circle of radius a. (e) Find the period of circular motion and the period of small radial oscillations. (f) Show that the nearly circular orbits are almost closed when a is very small
According to Yukawa’s theory of nuclear forces, the attractive force between a neutron and a proton has the potential V (r) = −Ke^(−αr)/r, K, α > 0 (a) Find the force, and compare it with an inverse square law of force.

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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
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 ...

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