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3. (10 points) in free space, E = 20xa, + 40yay-Oza, V/m. Calculate the work done in transferring a 2 mC charge along the arc r= 2,0 < φ < π/2 in the z = 0 plane.
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Answer #1

Solution :

Since work done in electric field only depends on the initial and final position, not on the path taken, i.e work done in eletric field is path independent..

Initial point : r = 2, phi = 0 corresponds to x = r*cos(phi) = 2, y =2*sin(phi) = 0.

Final Position ; r =2, phi = pi/2 corresponds to x = 0 , y = 2.

thus work done =   F.dr = q*E.dr

Please find attached the image for solution !

- 20 .120 x 4o 42 = 3

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