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

As we know that w = V/r and V_theta = wr (sin theta i^- cos theta J) V_theta = V(sin theta i^- cos theta J) from ground frame V_net = V^rightarrow i^+ V^riaghtarrow(sin theta i^- cos theta J^) Net force acting on charge particle F_net = q E J^+ q V B i^a = F/m = q E/m J^+ q V B/m i^dv/dt = q E/m J^+ q V B /m i^V = q E/m t J^+ q V B/m t + constant dv/dt = q E/m t J^+ q V B/m t + constant V = q E/2 M t^2 J^+ q V B/2m + q V B/2m t^2 + constant x(t) = q E/2m t^2 j^+ q v B/2m t^2 + constant x(t) = q E/2m t^2 J^+ q V B/2m t^2 + constant