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CBSE Class 12 Physics 2017 Delhi Set 3 Paper

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Question : 5 of 8
Marks: +1, -0
(i) Obtain the expression for the torque τ→\overset{\rightarrow}{\tau} experienced by an electric dipole of dipole moment p→\overset{\rightarrow}{p} in a uniform electric field, E→\overset{\rightarrow}{E}.
(ii) What will happen if the field were not uniform?
Solution:  
(i) Obtaining of the expression for torque experienced by an electric dipole
(ii) Effect of non-uniform electric field
(i)
Force on +q,F→=qE→+q, \overset{\rightarrow}{F}=q \overset{\rightarrow}{E}
Force on −q,    F→=−qE→-q, \;\; \overset{\rightarrow}{F}=-q \overset{\rightarrow}{E}
Magnitude of torque
τ  =qE×2asin⁡  θ\tau\;=q E \times 2 a \sin\;\theta
  =2qaEsin⁡  θ\;=2 q a E \sin\;\theta
τ→  =p→×E→\overset{\rightarrow}{\tau}\;=\overset{\rightarrow}{p}\times \overset{\rightarrow}{E}
(ii) If the electric field is non uniform, the dipole experiences a translatory force as well as a torque.
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