A21-Lect-10+%5BCompatibility+Mode%5D - 2/9/2009 29.3 The...

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2/9/2009 1 ¾ Fig (a) below shows a dipole placed in a uniform electric field. ¾ The forces exert a torque on the dipole, but now we are interested in finding the work done by these forces as the dipole rotates from angle φ to angle 29.3 The Potential Energy of a Dipole + F F r r and rotates from angle i f . ¾ Fig (b) shows the force on the positive charge, causes the dipole to rotate a small displacement. d d rd ds ) 2 1 ( = = ¾ Thus the small work done by + F r θ cos ) ( ds F s d F dW + + + = = r r d pE d qdE cos 2 1 cos 2 1 = = ¾ We have ¾ Thus the work done by the electric field on the dipole is, ¾ The total work as the dipole turns from sin ) 90 cos( cos 90 = + = + = o o d pE d pE dW dW elec sin ) 90 cos( 2 1 2 2 = + = = + o f i ¾ The potential energy that is associated with the work done is, ¾ B i th l ft d i ht id f th b t i f elec pE pE d pE W f i cos cos sin = = ( ) i f elec i f dipole pE pE f i W U U U cos cos + = = = By comparing the left and right sides of the eqn above we get, E p pE U dipole r r . cos = =
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2/9/2009 2 ¾ The fig shows the energy diagram of a dipole. At θ = 0, the potential energy is minimum, that’s when the dipole is aligned with field which represents a stable equilibrium point. ¾ At θ =± 180 ˚ , the dipole is exactly opposite the electric field, this point represents an unstable equilibrium any small disturbance will cause it to flip around.
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This note was uploaded on 02/21/2009 for the course PHY A10 taught by Professor Tawfiq during the Fall '08 term at University of Toronto.

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A21-Lect-10+%5BCompatibility+Mode%5D - 2/9/2009 29.3 The...

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