An insulating sphere with radius r=0.1m that carries total charge q=1nc (uniformly distributed). the center of the sphere is located 0.2m above a large plastic sheet that has a uniform surface charge density =-8nc/m2 on one side. find the location of all points where the resultant electric field is zero, or show that there are no such points.

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?