Selected comments on: HW4 (6/24/02)

005-008. Cycloid motion in a combined E and B fields where E is perpendicular to B.

• Critical velocity: v_c=E/B.
• Force in the co-moving frame: F’=q v’ ´ B.
• The radius of the circular orbit due to this force is: r = mv_c/qB.
• In the lab frame, it is a rolling motion, where the velocity of the center equals to the critical velocity.

v_c

	A”
A

• Show that in the lab frame the horizontal speed at A’ is: v=2v_c.
• Show that the radius of curvature at A’, R=4r. (Hint: mv²/R= qvB-qE=qv_cB. Solve for R)
• Show that the magnetic force does not do work.
• Show that the energy equation in cycloid motion is given by: (1/2) mv² + eEy=0.

013. Hint: use the work energy theorem: Review chapter 7 and 8. W^ext=K_f-K_i + U_f-U_i + W^dis_i->f. In the context of present problem, show that the theorem can be written as F^extd=K_f. Notice that for a rolling motion, K = (1/2)mv² (1+k), where the moment of inertial is given by I=(1/2)kmv². For a solid rod k=1/2.

B ´

v₂

v₁

v_i

019 Elastic collision of two electrons: K_i = K₁ + K₂