Concept explainers
A small rigid object carries positive and negative 3 .50-nC charges. It is oriented so that the positive charge has coordinates (–1.20 mm, 1.10 mm) and the negative charge is at the point (1.40 mm. –1.30 nun), (a) Find the electric dipole moment of the object. The object is placed in an electric field
(a)
The electric dipole moments of the objects.
Answer to Problem 26.50P
The electric dipole moments of the objects is
Explanation of Solution
Given info: The electric field is
Write the expression for the distance between the negative and positive charge particle.
Here,
Substitute
Thus, the distance between the point is
Write the expression for the electric dipole moments.
Here,
Substitute
Conclusion:
Therefore, the electric dipole moments of the objects is
(b)
The amount of torque acting on the objects.
Answer to Problem 26.50P
The amount of torque acting on the objects is
Explanation of Solution
Given info: The electric field is
From the part (a) the dipole moment for the charge carries rigid body.
Thus, the dipole moment of the charge carries rigid body is
Write the expression for the torque acting on the object.
Here,
Substitute
Conclusion:
Therefore, the amount of torque acting on the objects is
(c)
The potential energy of the object field system.
Answer to Problem 26.50P
The potential energy of the object field system is
Explanation of Solution
Given info: The electric field is
Write the expression for the potential energy of the object field system.
Substitute
Conclusion:
Therefore, the potential energy of the object field system is
(d)
The difference between the maximum and minimum potential energy of the system.
Answer to Problem 26.50P
The difference between the maximum and minimum potential energy of the system is
Explanation of Solution
Given info: The electric field is
Write the expression for the magnitude of the electric field.
Here,
Substitute
Write the expression for the magnitude of the electric dipole.
Here,
Substitute
Write the expression for the maximum potential energy of the object field system.
Substitute
Thus, the maximum potential energy is
Write the expression for the minimum potential energy of the object field system.
Substitute
Thus, the minimum potential energy is
Write the expression for the change in the maximum and minimum potential energy of the electric field.
Substitute
Conclusion:
Therefore, the difference between the maximum and minimum potential energy of the system is
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Chapter 26 Solutions
Physics for Scientists and Engineers, Volume 1, Chapters 1-22