a.) Suppose that there is a constant magnetic field in thexy-plane with magnitude 0.5 T, and a proton is moving with a speedof 3 × 10^5 m/s at a 45◦ angle relative to the field. What is themagnitude of the acceleration of the proton assuming it onlyexperiences the force due to the magnetic field?
b.) Inside of any microwave, there is a tube called a magnetronin which electrons orbit an approximately constant magnetic field.The electrons in the microwave complete 2.4 billion circular orbitsevery second, and this causes them to emit microwave radiationhaving a frequency of 2.4 GHz. What is the strength (magnitude) ofthe magnetic field inside of the magnetron?
c.) A long, straight wire carrying a 3 A current perpendicularto the xy-plane intersects the x-axis at x = −2 cm. Anotherstraight wire carrying a 3 A current perpendicular to the xy-planeintersects the x-axis at x = 2 cm. At what point(s) along thex-axis is the magnetic field zero if the two currents are in theopposite direction? If there are no such points, write “None†andshow your reasoning.
d.) Suppose that a stream of electrons is moving along astraight wire perpendicular to this page, and the stream is movinginto the page. We take the page to be in the xy-plane, and wesuppose that the wire along which the electrons are movingintersects the page at the origin. A proton is at point (x,y) = (0cm, 3 cm) and has velocity (vx, vy) = (5×10^4 m/s, 0 m/s). Will theproton’s path curve into the page, out of the page, or will it justkeep moving straight with its current velocity? Write either“into,†“out,†or “straight†in the answer box, and explain yourreasoning.
