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

Question

n this problem, you will be asked to use the given diagram(Figure 1) to calculate the work done by the electric field E_vec 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 vec F = vec E q. Recall that the work Wdone on an object by a constant force is W= Fd cos theta, where F is the magnitude of the force acting on the object, d is the magnitude of the displacement that the object undergoes, and theta is the angle between the vectors F_vec and d_vec. Consider a uniform electric field E_vec and a rectangle ABCD, as shown in the figure. Sides AB and CD are parallel to E_vec and have length L; let alpha be angle BAC. Now assume that the particle chooses a different way of traveling. Calculate the total amount of work W_ADC done by the electrostatic force on the charged particle as it moves from A to D to C. Express your answer in terms of some or all the variables E, q, L and alpha.

Explanation / Answer

Wadc = EqL

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