# Work done in moving a 1C positive charge from one point to another

• Abdulwahab Hajar
In summary, we are determining the work done by the electric field E = axX - ay2y in moving a unit positive charge from position p1 (-2,0,0) to position p2 (5,-1,3) using the equation W = -q∫⃗E⋅→dl. The integral takes into account infinitesimal displacements in the x, y, and z directions, with the integration limits determining the direction of the displacement. The negative sign in the equation for work comes from the definition of electric potential, and there is no negative sign in the definition of work done by a force.
Abdulwahab Hajar

## Homework Statement

Determine the Work done by the electric field E = axX - ay2y in moving a unit positive charge from position p1 (-2,0,0) to position p2 (5,-1,3) the distances are in m

## The Attempt at a Solution

I'm not really experienced with forums therefore my attempted solution is an attached image.https://scontent-lht6-1.xx.fbcdn.net/v/t34.0-12/15683157_1201819119912120_1486498649_n.jpg?oh=0aad954d8ecb161d62c98aa8d1d685e7&oe=585F5529
is my displacement vector in my solution correct ? I did it as such because I have +ve displacement in the ax direction and -ve displacement in the ay direction.

The general way to represent an infinitesimal displacement is ##\vec{dl} = dx \, \hat{a}_x + dy \, \hat{a}_y + dz \, \hat{a}_z ##. The quantities ##dx##, ##dy##, and ##dz## could be positive, negative, or zero depending on the direction of the displacement. When you integrate with respect to ##y## from 0 to -1, ##dy## will be negative. You should not write ##\vec{dl} = dx \, \hat{a}_x - dy \, \hat{a}_y + dz \, \hat{a}_z ## with a negative sign for the y component. This would imply that the y component of displacement would be in the ##+\hat{a}_y## direction when ##dy## is negative.

Also, can you explain why you have a negative sign in front of the integral in the expression ##W = -q\int{\vec{E} \cdot \vec{dl}}##? Keep in mind that you are asked to find the work done by the electric field, not the work done by an external agent.

Wow dude thanks for the reply..
W=−q∫⃗E⋅→dl well I got the minus from the book, it's just like −∫⃗E⋅→dl for electrical potential apparently..
Could you enlighten me perhaps and so as you said dl=dx^ax+dy^ay+dz^az always stands right the integration limits determine the rest .
Thank you sir

The definition of the work done by a force along a path from point ##a## to point ##b## is ##\int_a^b \vec{F} \cdot \vec{dl}##. There is no negative sign in the definition. Definitions of electric potential and electric potential energy will have a negative sign.

Awesome bro
Thanks a lot

## 1. What is work done in moving a 1C positive charge from one point to another?

The work done in moving a 1C positive charge from one point to another is the amount of energy required to move the charge against an electric field from its initial position to its final position. It is measured in joules (J) and is calculated by multiplying the magnitude of the charge (1C) by the potential difference (in volts) between the two points.

## 2. How is work done related to electric potential?

The work done in moving a 1C positive charge from one point to another is directly related to the electric potential difference between the two points. The greater the potential difference, the more work is required to move the charge between the points. This relationship is described by the equation W = qΔV, where W is work done, q is charge, and ΔV is potential difference.

## 3. Does the direction of the electric field affect the amount of work done?

Yes, the direction of the electric field does affect the amount of work done. If the direction of the electric field is the same as the direction of the charge's motion, then the work done is positive. However, if the direction of the electric field is opposite to the direction of the charge's motion, then the work done is negative. This is because the electric field either aids or opposes the movement of the charge.

## 4. Is work done in moving a 1C positive charge always positive?

No, work done in moving a 1C positive charge is not always positive. As mentioned earlier, the direction of the electric field can determine whether the work done is positive or negative. Additionally, if the potential difference between the points is zero, then no work is done as there is no energy required to move the charge between the points.

## 5. How is work done in moving a 1C positive charge different from work done in moving a negative charge?

The work done in moving a 1C positive charge is the same as the work done in moving a negative charge, as long as the magnitude and potential difference between the points are the same. However, the direction of the work done will be opposite, as the electric field will either aid or oppose the movement of the positive or negative charge, respectively.

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