What is the maximum distance and velocity of a charge in an electric field?

In summary, a charge of -0.061 C initially moving to the right with a velocity of 54m/s experiences a force of 888N/C to the right in an electric field. With a mass of 0.72 kg, the maximum distance the charge moves to the right can be found using the equation F=qE and the conservation of energy. The velocity when it returns to the origin and at x=5.75m can also be calculated using high school mechanics techniques.
  • #1
dminus
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Homework Statement



A charge of -0.061 C is intiialy moving to the right with a velocity of 54m/s. It is moving in an electric field of 888N/C to the right, and has a mass of 0.72 kg. What is the maximum distance the charge moves to the right? What velocity does it have when it returns to the origin? What velocity does it have at x=5.75m?


Homework Equations



I don't know how to start.



The Attempt at a Solution



I tried using the electric field E=kq/r2but I can't get the solution.

I been looking at this problem blankly for a good two hours now and I could not find anything with google. Here is the link to the problem and solution.

http://books.google.com/books?id=vN...the origin has a magnitude of 845 N/C&f=false

Page 96 question 3.46
 
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  • #2
This problem might sound a little harder than it actually is.

All you need to notice that an electric field exerts a force on a charged particle given by

[tex] \vec{F}=q\vec{E} [/tex]

Once you consider that force, the problem can be solved with the usual high school mechanics techniques. (conservation of energy, anyone?)
 
  • #3
Ty, I got the same solution as the book. I guess I was over thinking such a simple problem.
 

1. What is the maximum distance of charge?

The maximum distance of charge refers to the furthest distance at which an electric charge can exert its influence on another charge. It is also known as the maximum range of an electric field.

2. How is the maximum distance of charge calculated?

The maximum distance of charge can be calculated using the inverse square law, which states that the strength of an electric field is inversely proportional to the square of the distance from the source charge. The formula for calculating the maximum distance of charge is d = √(Q/4πε0E), where d is the maximum distance, Q is the source charge, ε0 is the permittivity of free space, and E is the electric field strength.

3. Does the maximum distance of charge depend on the type of charge?

Yes, the maximum distance of charge depends on the type of charge. The strength of an electric field is determined by the magnitude and sign of the charge. A positive charge will have a different maximum distance of charge compared to a negative charge.

4. Can the maximum distance of charge be greater than the size of the source charge?

Yes, the maximum distance of charge can be greater than the size of the source charge. This is because the electric field extends infinitely in all directions, and the strength of the field decreases as the distance from the source charge increases.

5. What factors can affect the maximum distance of charge?

The maximum distance of charge can be affected by several factors, such as the magnitude of the source charge, the permittivity of the medium, and the presence of other charges in the vicinity. The medium through which the electric field travels can also affect the maximum distance of charge, as some materials may have a higher or lower permittivity than free space.

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