Question

(a) define the term dielectric constant of a medium in terms of capacitance of a capicitor

(b) why does the electric field inside a dielectric decrease whhen it is placed in an external electric field

(c) an electrostatic field line cannot be discontinuous, why ?

(d) can two equipotencials ever intersect ?

(e) why are equipotencial surfaces perpendicular to field lines ?

Answer 1

(a)Dielectric constant, property of an electrical insulating material (adielectric) equal to the ratio of thecapacitance of a capacitor filled with the given material to thecapacitance of an identical capacitor in a vacuum without the dielectricmaterial.
(b)The external field induces dipole moment by stretching or re-orienting the molecules of dielectric. Net effect of these induced molecular dipole moment is the production of a fieldthat opposes the external field. So,dielectric gets polarised in opposite direction and, electric field inside dielectric decreases.
(c)An electrostatic field line is a continuous curve because a charge experiences a continuous force when traced in an electrostatic field. Thefield line cannot have sudden breaks because the charge moves continuously and does not jump from one point to the other. ... Hence, twofield lines never cross each other.
(d)No they cannot intersect each other because two different equipotentialsurface have different electric potential, so if they intersect then the point of intersection will have twodifferent potentials at the same point which is not possible.
(e)In this case the "altitude" is electric potential or voltage. Equipotential linesare always perpendicular to the electricfield. In three dimensions, the linesform equipotential surfaces. Movement along an equipotential surface requires no work because such movement is alwaysperpendicular to the electric field.