Problem 4 (practice): A mad scientist considers creating a roller coaster which would use a uniform electric field to accelerate the roller coaster cars at the start of the ride. One coaster car has a mass of 250 kg, and the scientist manages to place 0.003 C of charge on it. How strong of an electric field would they need in order to get the coaster to go from rest to a speed of 17 m/s within a distance of 20 meters?

A doubly charged ion is accelerated from rest to a kinetic energy of 31.5 keV by the electric field between two parallel conducting plates separated by 1.75 cm.  What is the electric field strength between the plates, in volts per meter?

A Proton Gun. You and your team are designing a device that creates a beam of high-velocity protons. The device consists of a parallelplate capacitor in which protons start at rest at the positive plate. The protons accelerate toward the negative plate, which has a hole through which some of the protons pass. The plates are separated by 5.6cm, and the potential difference between the plates is 5.2kv. (a) What are the kinetic energies of the protons when they pass through the hole? (b) What are the speeds of the protons when they pass through the hole? (c) What is the acceleration of the protons between the plates? (a) Number Units

To see why, compute the force of Earth’s gravity on an electron and compare it with the force exerted on the electron by an electric field of magnitude 14000 V/m (a relatively small field). Express your answer to two significant figures and include the appropriate units.

A simple and common technique for accelerating electrons is shown in the figure below, where a uniform electric field is created between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. O (a) Calculate the acceleration of the electron if the field strength is 7.96 x 10¹ N/C. m/s² (b) Why will the electron not be pulled back to the positive plate once it moves through the hole? O The force of gravity is too strong. The other side of the positive plate also has a negative charge. There is no field outside the plates.

An electron is to be accelerated in a uniform electric field having a strength of 1.90  106 V/m. (a) What energy in keV is given to the electron if it is accelerated through 0.810 m?_________ keV(b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV (as in the Stanford Linear Accelerator, which is actually smaller than this)? ________km

An electron is to be accelerated over a distance 3.84m in a uniform electric field having a strength of 6.04x 10 V m What distance is required to give the electron a kinetic energy of 6.74GeV (in m)? M 31

Two parallel, flat, conducting plates with equal but opposite charges are separated by a uniform layer of insulating material with a dielectric constant of 7.1 and a thickness of 1.7mmmm. The electric field in the dielectric material is 2.22MV/mMV/m. What is the magnitude, in microcoulombs per squared meter, of the surface charge density on the conducting plates? What is the magnitude, in microcoulombs per squared meter, of the surface charge density on the conducting plates?

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Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 5.3-cm-long massless string and are at rest on a frictionless surface. Each is charged to +1.7 μC. (a).  The string is cut. What is the speed of 2-g-cube when the cubes are far apart? (b). The string is cut. What is the speed of the 4-g-cube when the cubes are far apart?