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Electricity
16 Mar 2008 18:34:01 IST
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16 Mar 2008 19:00:29 IST
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I think it does not because
For simple harmonic motion you need inertia and restoring force.
In this case there is restoring force but no inertia.( A dipole does not have euther mass or momentom). Therefore it does not execute SHM. But suppose the Charges are acuumulated on a body of specific mass to make a dipole then it may execute periodic motion. But it would not be SHM. The condition for shm is that the restoring force must be proportional to the displacement from mean position.
For simple harmonic motion you need inertia and restoring force.
In this case there is restoring force but no inertia.( A dipole does not have euther mass or momentom). Therefore it does not execute SHM. But suppose the Charges are acuumulated on a body of specific mass to make a dipole then it may execute periodic motion. But it would not be SHM. The condition for shm is that the restoring force must be proportional to the displacement from mean position.
16 Mar 2008 19:11:06 IST
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Yes sure enough, but if you want to get that relationship, you need the driving forces to move the object to and fro. The conditions shown are from the original concepts that we had learned in SHM. Could you Please check it with any references? May be I am wrong. I hope I am not confused. See if you can get an example of SHM which does not follow these condition. I am really curious.
16 Mar 2008 19:44:57 IST
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assuming the question states direction of dipole moment n tht of field r same:
hence this amts to in a positive field a positive chrg on top,a neg chrg below it...if v resolve the force acting on it v c tht the force torque acting is proportional to -sin
-
..
hence it will execute shm
hence this amts to in a positive field a positive chrg on top,a neg chrg below it...if v resolve the force acting on it v c tht the force torque acting is proportional to -sin
-..hence it will execute shm
16 Mar 2008 22:29:59 IST
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c wat i mean is this:
1st of all in a field there is a dipole... only if the dipole moment n field r parallel a restorin torque acts..if they r antiparallel then the torque wud push it further awy from mean position..
to find out what i am saying...u jus draw a dig urself..
u will c tht it is the sin@ component tht provides thye torque needed...n u will get the torque directly proportional to sin@..
sin@ approx equals @ as @ v.small..the condition necessary for shm is torque proportional to @..which is satisfied here..
1st of all in a field there is a dipole... only if the dipole moment n field r parallel a restorin torque acts..if they r antiparallel then the torque wud push it further awy from mean position..
to find out what i am saying...u jus draw a dig urself..
u will c tht it is the sin@ component tht provides thye torque needed...n u will get the torque directly proportional to sin@..
sin@ approx equals @ as @ v.small..the condition necessary for shm is torque proportional to @..which is satisfied here..
16 Mar 2008 22:41:18 IST
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hey hey there will be shm and....
see this is my thinking,.....
since the electric field is uniform.... the value of torque will be
=pEsin
but since angle is small we have......
=pE
this shows that torque is directly prop. to the angular disp...
and hence the motion due to this torque will be an angular shm one...
now since=pE ,
and so torque is directly proportional to...
and the constant of proprtionality k=pE
but k= I(omega)^2..
hence I(omega)^2=pE
and hence frequency of this shm is (1/2Pi)(under root of (pE/I))
see this is my thinking,.....
since the electric field is uniform.... the value of torque will be
=pEsinbut since angle
is small we have......=pE this shows that torque is directly prop. to the angular disp.
..and hence the motion due to this torque will be an angular shm one...
now since
=pE ,and so torque is directly proportional to
...and the constant of proprtionality k=pE
but k= I(omega)^2..
hence I(omega)^2=pE
and hence frequency of this shm is (1/2Pi)(under root of (pE/I))
20 Mar 2008 23:19:58 IST
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computer 001 your arguments are perfect. All the necessary condition for SHM are shown. And I accept it. But still I tell you one little secret, whenever i workout this question(Which i do almost every year) i tell the students that it does not follow shm for two reasons.
1. Many of the students they do not check the necessary condition for SHM in such cases. For them any periodic motion is SHM.
2. Theoretically it is less robust to assume, when explaining electrostatics, that charges are asociated with paricles alone. Because many of the basic theorems in electrostatics do not require that charges are associated with mass.
In every case since you have considered all the details, i accept your solution absolutely.
1. Many of the students they do not check the necessary condition for SHM in such cases. For them any periodic motion is SHM.
2. Theoretically it is less robust to assume, when explaining electrostatics, that charges are asociated with paricles alone. Because many of the basic theorems in electrostatics do not require that charges are associated with mass.
In every case since you have considered all the details, i accept your solution absolutely.
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it will execute torque if it is deflected to an angle