Question

5. An electron carrying charge -9 (where q=1.602e-19 C) is moving along the x axis in the +x direction with a velocity ū(x, y, z) = 5 x 107 cm/s. a. We want to make the electron to curve to the right and eventually go in a circle clockwise in the xy plane by applying a magnetic field. To achieve that, the magnetic field should exert a force on the electron that is perpendicular to its direction of motion. Which direction should the magnetic field point? Sketch a diagram of the velocity, magnetic field, and the Lorenz force exerted on the electron. Express your answer in terms of i, , 2 and their sign. b. We want the radius of the circle traced by the electron to be R=10 m. What is the magnitude of the magnetic field required to maintain the electron in this circular orbit? Hint: the Lorenz force exerted on the electron by the magnetic field should exactly equal (and oppose) the centrifugal force on the electron F=mv2/R.

Answer 1

Solution (a a charge charge on on electron - 1.602 x o c torentz force - V = 5x10t q. (JxB) 2 cm/sec 1 At point for clock wise force should be in -g direction. field in a directiay. So, we need magnetic ke can use product or Cross right hand rule. O out ward in ward + magnetic field magro chagnetic field. a magnetic field

lorentz Ponce = a CVXB) - centrifugal Porce mue mass of deatson J 1'602x rolex sy B - 91803 602* 10 X 5410X B gal klost 1810 x 510 x 58107 roxloo A B = 9.1 x 103 * 5x107 loxloo x 1.602x15 19. - 5.68X108 Tesla.