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Question:

Deduce the expression for the torque acting on a dipole of dipole moment →p in the presence of a uniform electric field →E. Consider two hollow concentric spheres, S1 and S2, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere S1 change if a medium of dielectric constant 'εr' is introduced in the space inside S1 in place of air?

Solution:

(a)Torque due to force acting on +q is τ1=−qEd2sinθ ^kTorque due to force acting on -q is τ2=−qEd2sinθ ^kTotal torque acting on dipole is τ=τ1+τ2τ=−qEdsinθ ^kτ=→p×→E(b)(i)Flux enclosed in S1, Φ1=2QεoFlux enclosed in S2, Φ2=6QεoRatio of flux, Φ1Φ2=13(ii)For medium εr,Flux enclosed in S1, Φ1=2QεoεrHence, flux enclosed will reduce.