Kinematics (electric force)

Problem:

An electron is released from rest at one point in a uniform electric field and moves a distance of 10 cm in 10-7 s.  What is the electric field strength and what is the voltage between the two points?

Solution:

Problem:

A proton is accelerated, in vacuum, from rest through a potential U and directed horizontally at a point midway between two horizontal parallel plates which are separated by 0.80 cm and 5 cm long.  An electric field is established between the plates by a 10 kV voltage supply and causes downward deflection.  Find the minimum accelerating potential U that will avoid the proton striking the lower plate.

Solution:

Problem:

A Wideroe linear accelerator consists of a series of cylinders connected to an alternating voltage.  A charged particle is accelerated during its passage through the gaps between the cylinders.  Inside the cylinders there is no acceleration.  The gaps all have equal lengths d, but the lengths of the cylinders, which are much longer than d, are chosen so that particles arrive at the gaps at the right phase of the alternating voltage to be accelerated.  Let there be N cylinders.  Find the length of the nth cylinder for a proton to be accelerated to the energy of 100 MeV if the frequency of the accelerating voltage is 150 MHz and if the acceleration across each gap is assumed to be constant. 

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Solution: