Dipole in a nonuniform electric field problem

In summary, a point charge Q is held at a distance r from the center of a dipole with charges ±q separated by s. When released, the dipole experiences a force with a net y-component of Qqs/(4πε0(r^2+s^2/4)^3/2). This assumes that r≫s.
  • #1
BrainMan
279
2

Homework Statement


A point charge Q is held at a distance r from the center of a dipole that consists of two charges ±q separated by a distance s. The dipole is initially oriented so that Q is in the plane bisecting the dipole. Assume that r≫s.

A) Immediately after the dipole is released, what is the magnitude of the force on the dipole?

B) Immediately after the dipole is released, what is the magnitude of the torque on the dipole?

Homework Equations

The Attempt at a Solution


[PLAIN]https://lh3.googleusercontent.com/krQ_JEzmRURs4ZqAkRwrapePDCVyz9DBcELyMJ8-tY1g2JYfSLGdkD4lv4_F_2FaaeXrNoN-ZofGqnvD3VNp8AgsogPnk_kYrS2RL9SY5A6K-q9RTfBwq5_Nv_exlvGk5w_Ui0p2kXAdQa1Jw005jR1eRS9G-0lFjnzhD7CfsHB8-pmm0Kxj-BRM_MQbHapBvyIVizorUYPVqCZNcPo1I8I0u83mzPTSJJdylwMoiC2qDsochCphoyNwRT62P_0p_VF0SKk2qpIhhLIdGO9EUow30nxJjp4EvvSKOMZGSaHl-aXsbewtiwn9ky2DmswaV_GOlaW2UFAhDKbytrYhK9GJ-kyP_PLobfQ_jyhIkKldBX29OF8DUKXyodk6Q4n3N5aW1X10msWQ_tzuchKdsmubrePdPNWxTWIHfLr4z9PL4NeXi5BaCm7QSaWWAyAWmRTkJwUx7AE9zwLyqdBmrwSxZIgZlK2z5_LM8rlKqCK3XdixKgaDBS9tOzi4wLe9Gp96Jn7gJpG_m5EwwgaA3LVHTWIWAWFvqzb_FXTW86j-81g_mAdb2Xltz2xyBYoA_Ozaai1Q46fI5-cPOp7f_rezMCPQ5gmLG-jD6g6m-KSyFMMzCkuT=w497-h662-no[/B]

I treated the two charges on the dipole as point charges and then found the force vectors acting on them. Then I broke down the forces into their components and added them. The x components canceled and I was left with just a y component. For some reason this is wrong, though.
 
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  • #2
It is not easy to read what the y-component is. Can you use LaTeX to write it down? I agree that the x-component is zero.
 
  • #3
kuruman said:
It is not easy to read what the y-component is. Can you use LaTeX to write it down? I agree that the x-component is zero.

Here is the net y-component of the force.

[tex] \frac{Qqs}{4\pi\epsilon_{0}(r^2+\frac{s^2}{4})^{3/2}} [/tex]
 
  • #4
I suspect that they want you to incorporate their specified assumption: Assume that r≫s
 
  • #5
gneill said:
I suspect that they want you to incorporate their specified assumption: Assume that r≫s
Exactly what I was about to type in. Before you do that, factor out of the radical r in the denominator.
 

1. What is a dipole in a nonuniform electric field?

A dipole in a nonuniform electric field is a system where two equal and opposite charges are separated by a distance in an electric field that is not uniform. This can occur when the electric field is stronger on one side of the dipole than the other, causing a net force on the dipole.

2. How is the force on a dipole in a nonuniform electric field calculated?

The force on a dipole in a nonuniform electric field can be calculated using the formula F = pE, where F is the force, p is the dipole moment, and E is the electric field. The dipole moment is calculated by multiplying the magnitude of the charges by the distance between them.

3. What is the torque on a dipole in a nonuniform electric field?

The torque on a dipole in a nonuniform electric field is the rotational force that is exerted on the dipole due to the nonuniform electric field. It is calculated by multiplying the dipole moment by the cross product of the electric field and the vector from the center of the dipole to the point where the force is being calculated.

4. How does the direction of the dipole affect its motion in a nonuniform electric field?

The direction of the dipole affects its motion in a nonuniform electric field because the force and torque on the dipole will depend on the orientation of the dipole relative to the electric field. If the dipole is aligned with the field, there will be no net force or torque, but if it is not aligned, there will be a net force and torque causing the dipole to move.

5. Can a dipole reach equilibrium in a nonuniform electric field?

Yes, a dipole can reach equilibrium in a nonuniform electric field. This occurs when the net force and torque on the dipole are equal to zero, meaning there is no longer any movement or rotation of the dipole. This can happen when the dipole is properly oriented and the electric field is balanced on both sides of the dipole.

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