Question

Question 2

Write down the equations of motion of a bead on a wheel:

(a) from the frame of the wheel

(b) from the frame of the ground

(c) Write the equations of motion of a charged particle q in a static electric field that is orthogonal to a magnetic field. Recall: F = q(E + V x B) Lorentz force law. Hint: mimic the derivation for a charged particle in a magnetic field. You should get x'' = -$\omega$²x + $\omega$ ²(E/B)t which has the solution x(t) = A₁cos$\omega$t + A₂sin$\omega$t + (E/B)t

Answer 1

a) From wheel frame V_1 = V (sin theta i^^- cos theta j^^) b) From ground frame V_2 = Vi^^+ V (sin theta i^^- cos theta j^^) = V (1 + sin theta)i^^- V cos theta j^^c) Force on charged particle F = qEj^^+ qVBi^^q = F/m = qE/m j^^+ qVBi^^x�� = d^2 x/dt^2 = qE/m j^^+ qVB/m i^^and we know x(t) = vt + 1/2 qt^2 x�� = -w^2 x + w^2 (E/B t where w^2 = 2/m