Work Done on Charge +q at Distance D from Semi-Infinite Grounded Metal

In summary, the conversation discusses the work done in bringing a charge +q from infinity in free space to a position at a distance D in front of a semi-infinite grounded metal surface. The formula for calculating the force is given, but there is confusion about the meaning of a semi-infinite grounded metal and the appearance of (2d*d) in the denominator. The concept of image charges is mentioned as a possible explanation.
  • #1
vrinda mukund
37
0

Homework Statement



The work done in bringing a charge +q from infinity in free space to a postion at a distance D in front of a semi-infinite grounded metal surface?

The Attempt at a Solution


Actually i know the method to solve it, but didn't understand its logic.
F=[-1/(4pi*e0)](q*-q)/(2d*d)
When we integrate this F as integral of F.dr between the limits x= d and x= infinity we get the result.
my question is what is this semi infinite grounded metal? how does this (2d*d) appear in the denominator? des this q and -q appears because of induction charging ?
 
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  • #2
Isn't this the http://en.wikipedia.org/wiki/Method_of_image_charges" [Broken]?

Dont' know what's meant by a "semi-infinite" grounded metal though.

Maybe it's metal taking up half of all available space, and having a plane surface, like http://upload.wikimedia.org/wikipedia/commons/4/4c/Method_of_mirror_images.png" [Broken]. In that case, yeah the -q would be the induced charge. But it looks to me like it would be ((2x)*(2x)) instead of (2d*d) in the denominator, where x is the variable distance of the charge +q from the surface as it moves.
 
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1. What is "Work Done on Charge +q at Distance D from Semi-Infinite Grounded Metal"?

"Work Done on Charge +q at Distance D from Semi-Infinite Grounded Metal" refers to the amount of energy required to move a positive charge +q from a certain distance D away from a semi-infinite grounded metal to a desired location. This is a concept in electrostatics and is important in understanding the behavior of charged particles near conductors.

2. How is the work done on a charge calculated in this scenario?

The work done on a charge +q at distance D from a semi-infinite grounded metal can be calculated using the formula W = kqQ/D, where k is the Coulomb's constant, q is the charge of the particle, Q is the charge of the grounded metal, and D is the distance between the particle and the grounded metal. This formula takes into account the electrostatic force between the two charges.

3. Why is the metal considered "semi-infinite" in this scenario?

The metal is considered "semi-infinite" because it is assumed to be an infinite conducting plane with one side being grounded and the other side extending infinitely. This allows for simplification of the calculations and assumptions about the electric field in the vicinity of the metal.

4. How does the distance from the grounded metal affect the work done on the charge?

The work done on the charge is inversely proportional to the distance from the grounded metal. This means that as the distance increases, the work done decreases, and vice versa. This is because the electrostatic force between the charges decreases as the distance increases, resulting in less energy needed to move the charge.

5. Why is understanding the work done on a charge near a grounded metal important?

Understanding the work done on a charge near a grounded metal is important in various applications, such as in designing electronic circuits and in studying the behavior of charged particles in electric fields. It also helps in understanding the concept of electric potential and how it varies in different regions around a conductor.

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