How are they related? I have to find A doubly charged helium atom, whose mass is 6.6 10-27 kg, is accelerated by a voltage of 2600 V. (a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.380 T field? (b) What is its period of revolution? All I know is v(velocity)=E/B, V=IR, F=ILB. How can I find the radius of curvature?
you can solve both of these, once you know the velocity after the ion goes through the electric potential. Before crossing the potential, it has potential energy qV, so after it loses that potential energy by travelling to the other side of the electric field, by conservation of energy, we have qV=1/2mv<sup>2</sup>. its kinetic energy after it crosses the electric field is equal to the potential energy before it crosses the electric field, because all the potential energy is converted to kinetic energy, just like a ball rolling down a hill. now, for objects undergoing circular motion, we have F=mv<sup>2</sup>/r (this is the formula for centripetal force, which you learn in mechanics). you have the formula for magnetic force on a wire (F=ILB), so do you also have the formula for magnetic force on a point charge? it's F=qvB. substitute that formula into the first one, and solve for r r=mv/qB then just plug in v, which you get above by solving qV=1/2mv<sup>2</sup> then for the period of revolution, well, you know it goes through one revolution (2πr) every period (T), so speed is distance over time, v=2πr/T. solve for T
