How do you derive this (E=v/d)?

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In summary, the equation E = V/d can be derived from the relationship that electric potential is the negative of the line integral of the electric field, when the electric field and path are in the same direction. This can also be shown using the equation V = k(q/d), where V is the potential difference at a distance d from a charged particle q of a unit charge brought from infinity. By substituting q with (Ed2)/k, which is derived from the electric field at a point from a source charge q, the equation E = V/d can be derived.
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How do you derive this (E=v/d)?
 
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  • #3


aaaaa :biggrin: that sort of went over my head.

Can you do it with this relation -

V = k(q/d)

i.e potential difference at a distance d from a charged particle q of a unit charge brought from infinity.
 
  • #4


There's something wrong with latex...its showing my old codes.
 
  • #5


Yep got that --

In V = k(q/d) substitute q with (Ed2)/k (derived from E.F at a point from a source charge q)

Solve and you get it.
 

Related to How do you derive this (E=v/d)?

1. How did you come up with the equation E=v/d?

The equation E=v/d is derived from the fundamental equation for energy, E=Fd, where F represents force and d represents distance. By rearranging this equation to solve for v (velocity), we get E=v/d.

2. What is the significance of the variables v and d in the equation E=v/d?

The variable v represents velocity, which is the rate of change of an object's position. The variable d represents distance, which is the total amount of space an object has traveled.

3. Can you explain the relationship between energy, velocity, and distance in this equation?

The equation E=v/d shows that energy is directly proportional to velocity and inversely proportional to distance. This means that as an object's velocity increases, its energy also increases. On the other hand, as an object travels a greater distance, its energy decreases.

4. Is this equation applicable to all types of energy?

No, this equation is specifically applicable to kinetic energy, which is the energy an object possesses due to its motion. It does not account for potential energy or other forms of energy.

5. How can this equation be used in real-world applications?

The equation E=v/d can be used in various fields such as physics, engineering, and mechanics to calculate the kinetic energy of moving objects. It can also be used to analyze and optimize the efficiency of machines and systems that involve motion.

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