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Am electric dipole is placed in a uniform electric field . (i)Show that no traslatory force acts on it .(ii)Derive an expression for the torque acting on it.(iii)Find work done in rotating the dipole through 180^(@). |
Answer» Solution :Electric dipole of charges + q and - q separated by distance 2a is shown in figure. It is PLACED in a uniform electric FIELD at an angle `theta` with it. (i)Force on charge `+q,F_(1)=qvecE` , in the DIRECTION of `vecE`. Force on charge `-q,F_(2)=-qvecE`,in the opposite direction of E. `therefore` Net translatory force on dipole `=F_(1)+F_(2)` `=+qvecE-qvecE=0` HENCE , no translatory force acts on it. (ii)But the two equal parallel and unlike forces form a couple in which a torque is given by `TAU="Force"xx`perpendicular distance between the two forces `=qExx2asintheta` `tau=pEsintheta` where , `p=qxx2a=`dipole moment (iii)Work done in rotating the dipole through `180^(@)` is `W=intdW` `=int_(0^(@))^(180^(@))tau d theta=pEint_(0^(@))^(180^(@))sin theta d theta` `=pE[-costheta]_(0^(@))^(180^(@))` `=pE[cos180^(@)-cos0^(@)]` `=pE[1+1]=2pE` |
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