î × ƒ = k‚ ƒ × k = î, k×î=j, A× B = -B × A, |Ã× B|= AB sin 0, FB = qv×B,H R = = mv ‚ FÅ = IL × B. qB Problem 1: A proton (q B = = +e = +1.60 × 10-19 C) moves through a uniform magnetic field given by (0.011 -0.02ĵ+ 0.03) T. At this instant the proton has a velocity given by v = v×î + vyĵ + (2000 m/sec)k and the magnetic force on the proton is F = (4.0 × 10¯¹7N)î + (2.0 × 10¯¹7 N)ĵ. What are v and vy? Answer: vx = -3500 m/sec and vy = 7000 m/sec.

In the figure, an electron accelerated from rest through potential difference V₁-1.03 kV enters the gap between two parallel plates having separation d-17.2 mm and potential difference V₂-108 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit- vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number (0 7+0 3.30e-4 A) Units mT

In the figure, an electron accelerated from rest through potential difference V₁-1.12 kV enters the gap between two parallel plates having separation d = 21.0 mm and potential difference V₂= 129 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number ( i + k) Units

A small rod magnet has a magnetic field at a distance from it as large as Hom B = 2nz3 Where z is the distance from the magnet on the axis connecting the north pole and south, m is the moment of magnetic dipole. Assuming electrons orbit protons like small rod magnets, determine the m magnetic dipole of an electron orbiting an atom.