18.63 -Applications of Electrostatics Points: 1 In the figure below, four equal

Question

18.63 -Applications of Electrostatics Points: 1 In the figure below, four equal charges q 73.0 nC lie on the corners of a horizontal square. A fifth c n 3.5 g directly above the center of the square, at a height equal to the length d = 13.0 cm of one side of the square. etermine the magnitude of Q if the Coulomb force is to equal the weight of m. (Is this equilibrium stable or unstable? Discuss.) harge Q is on a mass 0 igure caption: Four equal charges on the corners of a horizontal square support the weight of a fifth charge located directly bove the center of the square. Submit Answer Tries 0/5

Explanation / Answer

distance from each corner to point O,

r = sqrt(d^2 + d^2/2)

= d*sqrt(3/2)

= 0.13*sqrt(3/2)

= 0.159 m

so, electric field due to each charge, E = k*q/r^2

= 9*10^9*73*10^-9/0.159^2

= 2.60*10^4 N/c

angle made by each elctric field with vertical, theta = tan^-1( d/(d/sqrt(2))

= tan^-1(sqrt(2))

= 54.7 degrees

so, Enet = 4*E*cos(theta)

= 4*2.60*10^4*cos(54.7)

= 6.01*10^4 N/c

now use, Fe = Fg

Q*Enet = m*g

Q = m*g/Enet

= 3.5*10^-3*9.8/(6.01*10^4)

= 5.71*10^-7 C or 0.571 micro C

stable equilibrium.

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