Work done by moving unit charge along straight line segment

In summary, the work done by moving a unit charge along a straight line segment is the amount of energy transferred to or from the charge as it moves from one point to another. This is measured in joules (J) and is directly related to the change in electric potential between the initial and final points. The unit of measurement for this work is the joule (J), but it can also be measured in electron volts (eV) or kilojoules (kJ). This work can be negative if the charge moves from a point of higher electric potential to a point of lower electric potential, indicating energy transfer to the surroundings. The work done is directly proportional to the distance traveled, meaning that a greater distance results in a greater amount
  • #1
tronter
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If [tex] \bold{F}(x,y) = \frac{k(x \bold{i} + y \bold{j})}{x^{2}+y^{2}} [/tex] find the work done by [tex] \bold{F} [/tex] in moving a unit charge along a straight line segment from [tex] (1,0) [/tex] to [tex] (1,1) [/tex].

So [tex] \bold{F}(1,y) = \frac{k(\bold{i} + y \bold{j})}{1 + y^{2}} [/tex]. Then [tex] x = 1, \ y = y [/tex].

[tex] k \int_{0}^{1} \frac{y}{1+y^{2}} \ dy [/tex]

[tex] u = 1+y^{2} [/tex]

[tex] du = 2y \ dy [/tex]

[tex] \frac{k}{2} \int \frac{du}{u} [/tex]

[tex] = \frac{k}{2} \int_{0}^{1} \ln|1+y^{2}| [/tex]

[tex] = \frac{k\ln 2}{2} [/tex].

Is this correct?
 
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  • #2
Looks perfectly good to me.
 

FAQ: Work done by moving unit charge along straight line segment

1. What is work done by moving unit charge along a straight line segment?

The work done by moving a unit charge along a straight line segment is the amount of energy transferred to or from the charge as it moves from one point to another. This is typically measured in joules (J).

2. How is work done by moving unit charge related to electric potential?

The work done by moving a unit charge is directly related to the change in electric potential between the initial and final points. This relationship is given by the equation W = qΔV, where W is the work done, q is the charge, and ΔV is the change in electric potential.

3. What is the unit of measurement for work done by moving unit charge?

The unit of measurement for work done by moving a unit charge is the joule (J). However, in some cases, it may also be measured in electron volts (eV) or kilojoules (kJ).

4. Can the work done by moving unit charge be negative?

Yes, the work done by moving a unit charge can be negative if the charge moves from a point of higher electric potential to a point of lower electric potential. This indicates that energy is being transferred from the charge to its surroundings.

5. How does distance affect the work done by moving unit charge?

The work done by moving a unit charge is directly proportional to the distance traveled. This means that the greater the distance between the initial and final points, the greater the work done. This relationship is given by the equation W = Fd, where F is the force on the charge and d is the distance traveled.

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