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An electric dipole rotates at constant angular velocity ?

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 21P Chapter 11

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 21P

An electric dipole rotates at constant angular velocity ω in the x y plane. (The charges, ±q, are at  the magnitude of the dipole moment is p = 2qR.)

(a) Find the interaction term in the self-torque (analogous to Eq. 11.99). Assume the motion is nonrelativistic (ωR ≪ c).

(b) Use the method of Prob. 11.20(a) to obtain the total radiation reaction torque on this system.

(c) Check that this result is consistent with the power radiated (Eq. 11.60).

Reference equation 11.60

Reference equation 11.99

Reference prob 11.20

Deduce Eq. 11.100 from Eq. 11.99. Here are three methods:

(a) Use the Abraham-Lorentz formula to determine the radiation reaction on each end of the dumbbell; add this to the interaction term (Eq. 11.99).

Step-by-Step Solution:

Step 1 of 4</p>

Part a

We are required to calculate the interaction term in the expression for torque assuming the motion to be nonrelativistic.

We are first required to calculate the electric field at the charge  for the charge .

Let us check the following figure to understand the situation.

We get ,

At the point , the velocity of the charge is,

So, the acceleration,

We have the electric field equation,

Now,

             

Step 2 of 4</p>

Therefore, the equation for electric field,

   

The torque,

   

 

Here,

Now,

The torque,

Now,

Now, is can be expressed as ,

And,

Therefore, the torque

Step 3 of 4

Chapter 11, Problem 21P is Solved
Step 4 of 4

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

The answer to “An electric dipole rotates at constant angular velocity ? in the x y plane. (The charges, ±q, are at the magnitude of the dipole moment is p = 2qR.)(a) Find the interaction term in the self-torque (analogous to Eq. 11.99). Assume the motion is nonrelativistic (?R ? c).(b) Use the method of Prob. 11.20(a) to obtain the total radiation reaction torque on this system.(c) Check that this result is consistent with the power radiated (Eq. 11.60).Reference equation 11.60 Reference equation 11.99 Reference prob 11.20Deduce Eq. 11.100 from Eq. 11.99. Here are three methods:(a) Use the Abraham-Lorentz formula to determine the radiation reaction on each end of the dumbbell; add this to the interaction term (Eq. 11.99).” is broken down into a number of easy to follow steps, and 116 words. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. The full step-by-step solution to problem: 21P from chapter: 11 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. Since the solution to 21P from 11 chapter was answered, more than 229 students have viewed the full step-by-step answer. This full solution covers the following key subjects: reference, reaction, torque, term, dipole. This expansive textbook survival guide covers 12 chapters, and 550 solutions.

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