I need help solving this problem. A small, rigid object carries positive and neg
ID: 1534079 • Letter: I
Question
I need help solving this problem.
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, 1.40 mm) and the negative charge is at the point (1.30 mm, -1.30 mm). Find the electric dipole moment of the object. The object is placed in an electric field E = (7.80 times 10^3 l - 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. Assuming the orientation of the object can change, find the difference between the maximum and the minimum potential energies of the system.Explanation / Answer
Given
charge of rigid body is (dipole ) is 2 nC
we know that dipole is equal and opposite charges separated by a distance and the direction of dipole moment vector is from -ve charge tp +ve charge
the position is +ve charge at (-1.2 mm, 1.4mm), -ve charge at (1.3mm, -1.3 mm)
a)
the dipole moment vector is Pbar = q*d i +q*d j
P = 2*10^-9(-1.2*10^-3 - 1.3*10^-3) i+ 2*10^-9(1.4*10^-3 +1.3*10^-3) j
P = 2*10^-9(-2.5*10^-3)i +2*10^-9(2.7*10^-3)j
P = -5*10^-12 i + 5.4*10^-12 j
P = sqrt((-5*10^-12)^2+(5.4*10^-12)^2)
magnitued is P = 7.35935*10^-12 C.m
Electric field is E = (7.8*10^3 i -4.9*10^3 j) N/C
b)
now the torque T = P X E = PEsin theta
T = 0 i + 0 j + (-5*10^-12)(-4.9*10^3) -(5.4*10^-12*7.8*10^3) k
T = 0 i + 0 j - 1.762*10^-8 k
the angle between the vectors is theta
theta = arc cos (P.E/(magP)(mag E))
= arc cos ((-5*10^-12*7.8*10^3)(5.4*10^-12*-4.9*10^3)/((7.35935*10^-12)*(9211.4059730314784)))
c) = 89.99 degrees = 90 degrees
so potential energy of the system is U = P.E = PEcos theta = P.E cos 90 = 0J
d) max potential energy is Umax = P.E = 1.03194*10^-15 J, minimu U = 0J
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