Assignment 3 Are Coulomb Forces Conservative? « previous 9 of 15 next » Are Coul
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Assignment 3
Are Coulomb Forces Conservative?
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Are Coulomb Forces Conservative?
Learning Goal:
To review the concept of conservative forces and to understand that electrostatic forces are, in fact, conservative.
Such forces are called conservative forces. If only conservative forces act within a closed system, the total amount of mechanical energy is conserved within the system (hence the term "conservative"). Such forces have a number of properties that simplify the solution of many problems.
Not all forces that we deal with are conservative, of course. For instance, the amount of work done by a frictional force very much depends on the object's trajectory. Friction, therefore, is not a conservative force. In contrast, the gravitational force is the most common example of a conservative force. What about electrostatic (Coulomb) forces? Are they conservative, and is there a potential energy function associated with them?
In this problem, you will be asked to use the given diagram(Figure 1) to calculate the work done by the electric field E on a particle of charge q and see for yourself whether that work appears to be trajectory-independent. Recall that the force acting on a charged particle in an electric field is given by F =E q.
W=Fdcos,
Consider a uniform electric field E and a rectangle ABCD, as shown in the figure. Sides AB and CD are parallel to E and have length L; let be angle BAC.
Part A
Calculate the work WAB done by the electrostatic force on a particle of charge q as it moves from A to B.
Express your answer in terms of some or all the variables E, q, L, and .
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Correct
The angle between the force and the displacement is zero here, so cos=1, and the general formula for work becomes W=Fd.
Part B
Calculate the work WBC done by the electrostatic force on the charged particle as it moves from B to C.
Express your answer in terms of some or all the variables E, q, L, and .
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Correct
Now the angle between the force and the displacement is 90, so cos=0, and the work done is zero.
Part C
Calculate the total amount of work WABC done by the electrostatic force on the charged particle as it moves from A to B to C.
Express your answer in terms of some or all the variables E, q, L, and .
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Part D
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Part E
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Figure 1 of 1
Correct. Followup. Now the angle between the force and the displacement is 90, so , and the work done is zero. End of followup.
Are Coulomb Forces Conservative?
Learning Goal:
To review the concept of conservative forces and to understand that electrostatic forces are, in fact, conservative.
As you may recall from mechanics, some forces have a very special property, namely, that the work done on an object does not depend on the object's trajectory; rather, it depends only on the initial and the final positions of the object.Such forces are called conservative forces. If only conservative forces act within a closed system, the total amount of mechanical energy is conserved within the system (hence the term "conservative"). Such forces have a number of properties that simplify the solution of many problems.
You may also recall that a potential energy function can be defined with respect to a conservative force. This property of conservative forces will be of particular interest of us.Not all forces that we deal with are conservative, of course. For instance, the amount of work done by a frictional force very much depends on the object's trajectory. Friction, therefore, is not a conservative force. In contrast, the gravitational force is the most common example of a conservative force. What about electrostatic (Coulomb) forces? Are they conservative, and is there a potential energy function associated with them?
In this problem, you will be asked to use the given diagram(Figure 1) to calculate the work done by the electric field E on a particle of charge q and see for yourself whether that work appears to be trajectory-independent. Recall that the force acting on a charged particle in an electric field is given by F =E q.
Recall that the work W done on an object by a constant force isW=Fdcos,
where F is the magnitude of the force acting on the object, d is the magnitude of the displacement that the object undergoes, and is the angle between the vectors F and d .Consider a uniform electric field E and a rectangle ABCD, as shown in the figure. Sides AB and CD are parallel to E and have length L; let be angle BAC.
Part A
Calculate the work WAB done by the electrostatic force on a particle of charge q as it moves from A to B.
Express your answer in terms of some or all the variables E, q, L, and .
WAB = qELSubmitMy AnswersGive Up
Correct
The angle between the force and the displacement is zero here, so cos=1, and the general formula for work becomes W=Fd.
Part B
Calculate the work WBC done by the electrostatic force on the charged particle as it moves from B to C.
Express your answer in terms of some or all the variables E, q, L, and .
WBC = 0SubmitMy AnswersGive Up
Correct
Now the angle between the force and the displacement is 90, so cos=0, and the work done is zero.
Part C
Calculate the total amount of work WABC done by the electrostatic force on the charged particle as it moves from A to B to C.
Express your answer in terms of some or all the variables E, q, L, and .
WABC =SubmitMy AnswersGive Up
Part D
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Part E
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Part F
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Part G
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Figure 1 of 1
Explanation / Answer
a)
from
W=Fdcos(o)
=>WAB=(qE)L*cos0=qEL
b)
WBC=qELcos90
WBC=0
c)
WABC=qELcos0
WABC=qEL