A small, rigid object carries positive and negative 2.00 nC charges. It is orien

Question

A small, rigid object carries positive and negative 2.00 nC charges. It is oriented so that the positive charge has coordinates (-1.20 mm, 1.60 mm) and the negative charge is at the point (1.90 mm, -1.30 mm). Find the electric dipole moment of the object. The response you submitted has the wrong sign. C middot m I + The response you submitted has the wrong sign. C middot m J The object is placed in an electric field E = (7.80 times 10^3 I - 4.90 times 10^3 J) N/C. Find the torque acting on the object. Find the potential energy of the object-field system when the object is in this orientation. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Assuming the orientation of the object can change, find the difference between the maximum and the minimum potential energies of the system. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. J

Explanation / Answer

Given
  
   the electric dipole of length l = sqrt((1.9 -(-1.2))^2+(-1.3-1.6)^2) mm = 4.245 mm

   charge q = 2 nC

the dipole moment is p = q*l = 2*10^-9 *4.245*10^-3 C m = 8.49*10^-12 Cm

a)
P = pi+pj

= 2*10^-9(-1.2-1.9)*10^-3 i + 2*10^-9(1.6+1.3)*10^-3

   Pi = (-6.2)*10^-12 C m

   Pj = 5.8*10^-12 C m

b)
   E = (7.8*10^3 i - 4.9*10^3 j) N/C

   torque acting on dipole is T = P X E = P E sin theta

the angle between the vectors is theta = arc cos (P.E/magP*magE)

P.E = ((-6.2)*10^-12*7.8*10^3)+(5.8*10^-12*(- 4.9*10^3))= (-7.678)*10^-8

mag P = 8.49*10^-12 C.m, mag E = sqrt((7.8*10^3)^2+(- 4.9*10^3)^2) N/C

           mag E   = 9211.41 N/C

now theta = arc cos ((-7.678)*10^-8/((8.49*10^-12 )(9211.41) ))

   theta = 169 degrees

now torque T = P*E sin theta
  
T = (-7.678)*10^-8(9211.41)sin169 = -0.000134950055 Nm

potential energy is U = pe cos theta = (-7.678)*10^-8(9211.41)cos169 J = 0.0006942578474 J

the maximum U = P*e = (-7.678)*10^-8 J

minimum is zero J

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