In this problem, you will be asked to use the given diagram(Figure 1) to calcula

Question

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 is

W=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 ?.

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 ?.

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 ?.

In this problem, you will be asked to use the given diagram(Figure 1) to calculate the work done by the electric fieldE? 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 is W=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 vectorsF? 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.

Explanation / Answer

A)

WOrk done in B to A = Force * distance

Work done = E*q*L

work done is EqL

B)

Now , Work done in B to C = Force * distance * cos(90)

Work done in B to C = qE*L*cos(90)

Work done in B to C = 0 J

C)

WOrk done in A to B to C = W(AB) + W(BC)

WOrk done in A to B to C = qE*L

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