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(a) Deduce the expression for the torque acting on a dipole of dipole moment vecP in the presence of uniform electric field vecE. (b) Consider two hollow concentric spheres, S_(1) and S_(2), enclosing charges 2Q and 4Q respectively as shown in the figure. |
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Answer» Solution :(a) Dipole in a uniform external field : Consider an electric dipole consisting of charge`-q and +q` and of length 2A placed in a uniform electric field `vecE` making an angle * with electric field. Force on charge -q at `A=-q" " vecE("opposite to " vecE)` Electric dipole is under the action of two equal and unlike parallel forces, which give rise to a torque on the dipole.  `tau="Force"xx"perpendicular idstance between the forces"` `tau=qE(AN)=qE(2a sintheta)` `tau=q(2a)E sintheta` `tau=pE sintheta` `therefore""tau=vecPxxvecE` (b)(i) Charge ENCLOSED by sphere `S_(1)=2Q`. by Gauses law, electric flux through sphere `S_(1)` is `phi=2thetaepsi_(0)` Charge enclosed by sphere, `S_(1)=2Q+4Q=6Q` `phi_(1)=6theta//epsi_(0)` The ratio of the electric flux is `phi_(1)//phi_(2)=2Qepsi_(0)//6Qepsi_(c)=(2)/(6)=(1)/(3)` (ii) For sphere `S_(1),` the electric flux is `phi'=2Q//epsi_(r)` `phi'//phi_(1)=(2theta)/(inr)divide (6theta)/(in_(0))=(in_(0))/(inr)*(1)/(3)` `therefore epsi_(r)gtepsi_(0),phi,ltphi_(1)` ltbr. Therefore, the electric flux through the sphere `S_(1)` decreases with the introduction of the dielectric INSIDE it. |
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