two particles, carrying chargees -q and +q and having equal masses m each,are fixed at the ends of a light rod of length 'a' to form a dipole.the rod is clamped at an end and is placed in a uniform electric field E with the axis of the diploe along hte electric field.The rod is slightly tilted and then released.Neglecting gravity find the time period of small oscillations.please explain the answer step by step with a digram....please

Asked by Sounak das | 24th May, 2014, 12:25: AM

Expert Answer:

 
Dipole moment p is given by p = qd . if this dipole is placed in electric field, it experiences a torque τ = p x E
 
begin mathsize 12px style tau space equals space p space cross times space E space equals space p E space sin theta
tau space equals space I cross times alpha space comma space w h e r e space I space i s space m o m e n t space o f space i n e r t i a space a n d space alpha space i s space a n g u l a r space a c c e l e r a t i o n
I cross times alpha space equals space I cross times fraction numerator d squared theta over denominator d t squared end fraction space equals space p E space sin theta space equals space p E space theta space left parenthesis space f o r space s m a l l space a n g u l a r space d i s p l a c e m e n t right parenthesis
h e n c e space fraction numerator d squared theta over denominator d t squared end fraction space equals space fraction numerator p E over denominator I end fraction theta

h e n c e space T space equals space 2 pi square root of fraction numerator I over denominator p E end fraction end root end style

Answered by  | 5th Jan, 2018, 04:13: PM