Insulator in an electric field

[Vibhor]

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]

I suppose the answers are A and C .A depicting the eletric field lines and C equipotential lines . Is it correct ?

I arrived at the answer by eliminating choices B and D . Since electric field lines cannot intersect ,option B was eliminated .Selecting A makes option C also correct .

But how do I be sure that A and C are correct options . What if there was a "None of these " options" ?

Please help me with the problem .

Thanks

 

[ehild]

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]

I suppose the answers are A and C .A depicting the eletric field lines and C equipotential lines . Is it correct ?

I arrived at the answer by eliminating choices B and D . Since electric field lines cannot intersect ,option B was eliminated .Selecting A makes option C also correct .

But how do I be sure that A and C are correct options . What if there was a "None of these " options" ?

Please help me with the problem .

Thanks

Think what happens when a dielectric sphere is placed into a homogeneous electric field, The external field polarises the dielectric, dipole chain arise so some of the initial electric field lines inside the sphere are "enclosed" in the dipole chains. The dipoles end at the surface of the sphere and produce surface charge, which opposes the external field near the sphere. Are the figures correspond to this behaviour? You also see in Fig A that the field lines in the dielectric sphere are parallel with the external field. Should it be so?

 

[Vibhor]

Thanks for replying .

Are A) and C) correct options ?

Think what happens when a dielectric sphere is placed into a homogeneous electric field, The external field polarises the dielectric, dipole chain arise so some of the initial electric field lines inside the sphere are "enclosed" in the dipole chains. The dipoles end at the surface of the sphere and produce surface charge, which opposes the external field near the sphere. Are the figures correspond to this behaviour?

I think A fulfills this behaviour . The electric field lines are normal to the surface where induced charges are present.

You also see in Fig A that the field lines in the dielectric sphere are parallel with the external field. Should it be so?

The magnitude of electric field inside the sphere should be less than outside . This is represented by density of field lines .This spacing between the field lines inside is more representing less EF strength inside.

But I am not confident whether field lines inside should be parallel with the external field ??

 

[ehild]

The polarization P is caused by the initial external field and it is parallel and proportional to that. The vector of dielectric displacement is D=ε₀E +P. Its normal component is continuous at the interface, while the tangential component of the electric field is continuous there. You can see where the surface of the sphere is normal to the original field, the bundary conditions dictate that the electric fields outside and inside are parallel.

I think this can be useful:
http://web.mit.edu/6.013_book/www/chapter6/6.6.html