= = > Consider a particle moving in a uniform magnetic field pointing in the z-direction: B = (0,0, B). From Feedback ex

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Consider A Particle Moving In A Uniform Magnetic Field Pointing In The Z Direction B 0 0 B From Feedback Ex 1 (314.04 KiB) Viewed 41 times

= = > Consider a particle moving in a uniform magnetic field pointing in the z-direction: B = (0,0, B). From Feedback exercises 1 we can choose the vector potential A : (0, B2,0) and the scalar potential p = 0. 2. Write the explicit form for the Hamiltonian function and Hamilton's equation. 3. The general solution to Hamilton's equations is x(t) = a + r sin(wt+c), y(t) = b+r cos(wt+c), z(t) = dt+e, where a, b, c, d, e,r are constants depending on the initial conditions. Find the explicit value of w. This is known as the cyclotron frequency. 4. Use conservation of energy to find the radius r. = = 2