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 ?.

Answer 1