A 24.41-mC charge is placed 38.65 cm to the left of a 80.73-mC charge, as shown

Question

A 24.41-mC charge is placed 38.65 cm to the left of a 80.73-mC charge, as shown in the figure, and both charges are held stationary. A particle with a charge of -7.551 mu C and a mass of 17.81 g (depicted as a blue sphere) is placed at rest at a distance 34.78 cm above the right-most charge. If the particle were to be released from rest, it would follow some complicated path around the two stationary charges. Calculating the exact path of the particle would be a challenging problem, but even without performing such a calculation it is possible to make some definite predictions about the future motion of the particle. If the path of the particle were to pass through the gray point labeled A, what would be its speed v_A at that point? A long, conductive cylinder of radius R_1 = 3.30 cm and uniform charge per unit length lambda 604 pC/m is coaxial with a long, cylindrical, non-conducting shell of inner and outer radii R_2 = 11.6 cm and R_3 = 13.2 cm, respectively. If the cylindrical shell carries a uniform charge density of rho = 53.6 pC/m^3, find the magnitude of the electric field at the following radial distances from the central axis:

Explanation / Answer

Change in KE = change in PE

= 9e9*-7.551e-6*[80.73e-3/0.3478 + 24.41e-3/sqrt(0.3865^2+0.3478^2) - 80.73e-3/(0.3478-0.1160) -24.41e-3/0.1160]

= 19004 J

v = sqrt(2PE/m)

= sqrt(2*19004/17.81e-3)

= 1461 m/s answer

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