A small, rigid object carries positive and negative 4.00 nC charges. It is orien

Question

A small, rigid object carries positive and negative 4.00 nC charges. It is oriented so that the positive charge has coordinates (1.20 mm, 1.40 mm) and the negative charge is at the point (1.70 mm, 1.30 mm).

(a) Find the electric dipole moment of the object.
C · m î +  C · m

(b) The object is placed in an electric field

Find the torque acting on the object.
N · m ---Select--- i j k

(c) Find the potential energy of the object–field system when the object is in this orientation.
J

(d) Assuming the orientation of the object can change, find the difference between the maximum and the minimum potential energies of the system.
J

Explanation / Answer

(a)

electric dipole moment P = d*q

d = seperation between charges from negative to positive

q = magnitude of charge

d = (-1.2 , 1.4) - (1.7 , -1.3)

d = (-1.2 - 1.7 , 1.4 + 1.3)

d = (-2.9 mm , 2.7 mm)

dipole moment P = q*d

P = -2.9*10^-3*4*10^-9 i + 2.7*10^-3*4*10^-9 i

P = -1.16*10^-11 i + 1.08*10^-11 j

==============================

(b)

torque = p x E

torque = (-1.16*10^-11 i + 1.08*10^-11 j) x ((7.80*10^3 i 4.90*10^3 j)

torque = -8.424*10^-8 i + 5.684*10^-8 k Nm

============================

potential energy U = -P.E ( P dot E ) dot product of E and P

U = -(-1.16*10^-11 i + 1.08*10^-11 j) . ((7.80*10^3 i 4.90*10^3 j)

U = -(-9.048*10^-8 - 5.292*10^-8)

U = 1.434 *10^-7 J

===================

difference = 2*1.434*10^-8 = 2.868 *10^-8J

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