A particle with charge q is located at the origin, and a particle with charge -3
ID: 1523583 • Letter: A
Question
A particle with charge q is located at the origin, and a particle with charge -3q is on the positive x axis, a distance d away from the origin. The particles are not free to move. In terms of q and d, at what coordinate should a third particle with charge a be placed so that it experiences n net electrostatic force? (assume r is the location of the third particle away from the origin, along the negative x axis.) A sphere has a net charge of 7.95 nc, and a negatively charged rod has a charge of -6.07 nc. The sphere and the nod undergo a process such that 5.80 times 10^9 electrons are transferred from the rod to the sphere. What are the charges of the sphere and the rod after this process? Two small metallic spheres, each with a mass of m = 8.00 g, are suspended from a common point by two strings of negligible mass of length L = 71.0 cm. When the spheres have an equal amount of charge, the two strings make an angle of 60 degree with each other as shown in the figure below. Calculate the magnitude of the charge on each sphere.Explanation / Answer
at the distance net force = 0
q1 = q
q2 = -3q
q3 = q
F13 + F23 = 0
k*q1*q3/r^2 + k*q2*q3/(r+d)^2 = 0
-k*q*q/r^2 + k*3q*q/(r+d)^2 = 0
1/r^2 = 3/(r+d)^2
(r+d)/r = sqrt3
1 + d/r = sqrt3
d/r = sqrt3 - 1
r = d/(sqrt3 - 1 ) = 1.37d<<<<=========ANSWER
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Q1(sphere) = 7.95 nC
Q2(rod) = -6.0 nC
amount of charge transferred Q = n*e = -5.8*10^9*1.6*10^-19 = -9.28*10^-10 C = -0.93 nC
charge on sphere = Q1 + Q = 7.95 - 0.93 nC = 7.02*10^-9 C <<<<=========ANSWER
Charge on rod = Q2- Q = -6 - (-0.93) = -5.07*10^-9 C <<<<=========ANSWER
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from the figure distance between the cahrges r = 2*L*sin30 = 2*0.71*sin30 = 0.71 m
electric force Fe = k*q^2/r^2
gravitational force Fg = m*g
IN equilibrium Fnet = 0
Fe = T*sin30
Fg = T*cos30
tan30 = Fe/Fg
tan30 = k*q^2/r^2m*g
tan30 = 9*10^9*q^2/(0.71^2*0.008*9.8)
q = 1.59 uC <<<<<=============ANSWER
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