3. Two uniformly charges rods each with a total charge Q = -8.00 MuC and length
ID: 1259851 • Letter: 3
Question
3. Two uniformly charges rods each with a total charge Q = -8.00 MuC and length L = 12.0 cm are arranged as shown below. Find the electric field at P if a = 4.25 cm. 4. Compute the work required to bring the following three charges from rest at an infinite separation to the following (x,y) locations: q1 = + 6.00 MuC at (0.0, 0.0) m, q2 = -3.00 MuC at (1.5, 0.0) m, and q3 = +4.0 0 MuC at (1.5, 5.0) m. Assume the charges are initially at rest and separated by an infinite distance. 5. After the charges in problem 4 are assembled the 6.00-MuC charge is released from rest. What is its kinetic energy when it is infinitely far from the other two charges?Explanation / Answer
3)
linear charge density, lamda = Q/L
= -8 micro C/0.12
= -66.7 micro C/m
Electric filed on the axis of the rod,
E = k*lamda*( 1/a - 1/(a+L) )
= 9*10^9*66.7*10^-6*(1/0.0425 - 1/(0.0425+0.12) )
= 1.043*10^7 N/c
Enet = (E^2 + E^2 + 2*E*E*cos(60))
= sqrt(3)*E
= 1.732*1.043*10^7
= 1.806*10^7 N/c
direction : 30 degrees with +x axis
4) initial potentail enrgy of the charge system, U1 = 0
fnal potentail enrgy of the charge system, U2 = k*q1*q2/r12 + k*q2*q3/r23 + k*q3*q1/r31
= -9*10^9*6*10^-6*3*10^-6/1.5 - 9*10^9*3*10^-6*4*10^-6/5 + 9*10^9*4*10^-6*6*10^-6/sqrt(1.5^2 + 5^2)
= -0.088 J
W = U2 - U1
= -0.088 J
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