0.25 m Problems 38 and 39 FIGURE 20-32 much work must be done to move the three

Question

0.25 m Problems 38 and 39 FIGURE 20-32 much work must be done to move the three char Figure 20-32 infinitely far from one another? a) Find the electric pot ose celeased from rest at point P. What is the speed of the fourth ential at point Pin FIGURE 20-33. (b) Sup- harge of +4.82 uC and a mass 40the three charges shown in Figure 20-33 are held in place. A fourth charge, with a c charge when it has moved infinitely far away from the other three of 2.33 g, charges? +7.45 C 1.25 m 1.25 m Pl 1.25 m 1.72 pC +2.75 C FIGURE 20-33 Problems 40 and 88 square of side a has a charge+Q at each corner. What is th A square of side a has eectric potential energy of this system of charges?

Explanation / Answer

a)The potential at point P will be the sum pf indivisual potentials due to the charges

V(P) = V1 + V2 + V3

V(P) = k q1/r1 + k q2/r2 + k q3/r3

r1 = r3 = 1.25/2 = 0.625 m

r2 = sqrt (1.25^2 - 0.625^2) = 1.083 m

V(P) = 9 x 10^9 x 10^-6 (2.75/0.625 + 7.45/1.083 - 1.72/0.625) = 7.67 x 10^4 V

Hence, V(P) = 7.67 x 10^4 V

b)The potential energy of the system is:

U = q V

U = 4.82 x 10^-6 x 7.67 x 10^4 = 0.369 J

from conservation of energy

1/2 m v^2 = 0.369

v = sqrt (2 x 0.369/m) = sqrt (2 x 0.369/(2.33 x 10^-3)) = 17.82 m/s

Hence, v = 17.82 m/s

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