a. Find an expression for the electric field strength |E| required to select a given speed |v| if the magnetic field inside the device has a magnitude |B|. Does your answer depend on the ion's mass m? Its charge q? (Hint: Assume you can ignore gravity). b. Find the value of |E| required to select protons with a speed of 0.01c (i.e. 0.01 times the speed of light) if |B| inside the device is 0.01 tesla. c. Explain why we can ignore gravity in the case of part b.
One can used crossed electric and magnetic fields to construct a velocity selector, a device that only passes charged particles having a certain specified velocity. The diagram shown illustrates one way of constructing such a velocity selector. We send an ion through a region of space where we have a uniform magnetic field perpendicular to the particles' velocity vector v and an electric field perpendicular to both vector B and vector v. Only ions having a specific speed will be able to travel in a straight line through this apparatus.
a. Find an expression for the electric field strength |E| required to select a given speed |v| if the magnetic field inside the device has a magnitude |B|. Does your answer depend on the ion's mass m? Its charge q? (Hint: Assume you can ignore gravity).
b. Find the value of |E| required to select protons with a speed of 0.01c (i.e. 0.01 times the speed of light) if |B| inside the device is 0.01 tesla.
c. Explain why we can ignore gravity in the case of part b.
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