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Coulomb-driven relativistic electron beam compression experiment setup. The laser is first split into two pulses with a beam splitter BS1 and then combined with a second beam splitter BS2. The high-energy pulse after pulse shaping is used to produce the drive beam, and the other low-energy pulse is used to produce the target beam. A solenoid lens is used to control the transverse size of the electron beam during beam propagation, and the electron beam longitudinal phase space is measured with an rf deflector and an energy spectrometer.
Current distribution shaded yellow area, bunch head to the right and the corresponding longitudinal Coulomb field solid line for the back drive beam a , for the front drive beam b , and when both drive beams are present c. Beam longitudinal phase space bunch head to the up as the total charge of the drive beams is gradually increased from 0. The top and bottom distributions show the front drive beam and back drive beam, and the target beam is in the middle. The corresponding electron beam temporal profiles are shown with solid white lines, and the rms bunch lengths are also given.
Note, due to the limited field of view of the screen, only part of the drive beam distribution is measured. Measured final energy and time of the target beam centroid with red dot and without magenta dot the drive beams. The simulation results are shown with black with drive beams and blue without the drive beams lines. The simulated longitudinal phase spaces for the drive beams is shown with blue dots. Measured pulse width and energy distribution for the target beam with 50 fC charge.
The 50 consecutive single-shot measurements of the target beam longitudinal profile without a and with c the drive beams, and the rms pulse width statistics collected over consecutive shots without b and with d the drive beams. The 50 consecutive single-shot measurements of the target beam energy distribution without e and with g the drive beams.
The centroid beam energy for each individual shot white circles is used to evaluate the energy jitter without f and with h the drive beams. It is much easier to perceive the gravitational force than the electrostatic force — mainly because the observed charges are usually balanced and have one charge equal to zero.
The forces which interact between protons and electrons, on the other hand, act in a microscopic way which is inaccessible to the human eye. It is known that the force increases with the value of the charges and the decrease in distance between them.
Coulomb's force is a vector quantity. Coulomb discovered that charge essentially has two natures: positive and negative. Whether they attract or repel each other depends on which charges we are dealing with. It is still known today that objects with the same charge as another object — either positive or negative — will repel each other. Objects with different charges, on the other hand, will attract each other.
The force studied by Coulomb, therefore, acts in two directions. But what happens if there are more than two objects? In which direction would the force then act? To this end, when presenting the formula for the electrostatic force, the discoverer of the law included an additional component to the equation, which is an indicator of the position of a specific, different charge.
History before the discovery of Coulomb's law. Even in the old days, it was already known that by rubbing amber against fur, the amber gained the ability to attract smaller objects. Through many types of research on this phenomenon, it was possible to accumulate bigger and bigger charges and transfer them from one object to another by touch.
All previous knowledge was limited to a series of experiments on ordinary objects until the discovery made by Charles Coulomb. Furthermore, we may extend this to the integral form. Substituting Equation 7. As a demonstration, from this we may calculate the potential difference between two points A and B equidistant from a point charge q at the origin, as shown in Figure 7.
This result, that there is no difference in potential along a constant radius from a point charge, will come in handy when we map potentials. Entering the given values for E and d gives.
The answer is quoted to only two digits, since the maximum field strength is approximate. Adding the two parts together, we get V.
Check Your Understanding From the examples, how does the energy of a lightning strike vary with the height of the clouds from the ground?
Consider the cloud-ground system to be two parallel plates. Before presenting problems involving electrostatics, we suggest a problem-solving strategy to follow for this topic. As an Amazon Associate we earn from qualifying purchases. Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4. Skip to Content Go to accessibility page. University Physics Volume 2 7. My highlights. Table of contents. Chapter Review.
Electricity and Magnetism. Answer Key. By the end of this section, you will be able to: Define electric potential, voltage, and potential difference Define the electron-volt Calculate electric potential and potential difference from potential energy and electric field Describe systems in which the electron-volt is a useful unit Apply conservation of energy to electric systems.
Calculating Energy You have a How much energy does each deliver? Assume that the numerical value of each charge is accurate to three significant figures. Strategy To say we have a When such a battery moves charge, it puts the charge through a potential difference of To find the energy output, we multiply the charge moved by the potential difference.
Appropriate combinations of chemicals in the battery separate charges so that the negative terminal has an excess of negative charge, which is repelled by it and attracted to the excess positive charge on the other terminal.
In terms of potential, the positive terminal is at a higher voltage than the negative terminal. Inside the battery, both positive and negative charges move. When a Strategy To find the number of electrons, we must first find the charge that moves in 1.
The energy of the electron in electron-volts is numerically the same as the voltage between the plates. For example, a V potential difference produces eV electrons. The conceptual construct, namely two parallel plates with a hole in one, is shown in a , while a real electron gun is shown in b.
Electrical Potential Energy Converted into Kinetic Energy Calculate the final speed of a free electron accelerated from rest through a potential difference of V. Assume that this numerical value is accurate to three significant figures. Strategy We have a system with only conservative forces.
Assuming the electron is accelerated in a vacuum, and neglecting the gravitational force we will check on this assumption later , all of the electrical potential energy is converted into kinetic energy. Dry air can support a maximum electric field strength of about 3.
Above that value, the field creates enough ionization in the air to make the air a conductor. This allows a discharge or spark that reduces the field. What, then, is the maximum voltage between two parallel conducting plates separated by 2. Strategy We are given the maximum electric field E between the plates and the distance d between them.
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