Couple of electromagnetics questions

[formulajoe]

E = 15 i - 8 k at a point on a conductor surface, what is the surface charge density at that point? assume Eo.

surface charge density is just -Eo*E correct? but i take the magnitude of the electric field and than multiply it by Eo.
am i right?

 

[dextercioby]

How come??What equation did you use...?

Daniel.

 

[formulajoe]

Gauss' Law

another quick question.

Region y is great than or equal to 2 is occupied by a conductor. If the surface charge on the conductor is -20 nC/M^2, find D just outside the conductor.
Since the surface is y = , than the normal would be in the y direction. and D = Eo*E. but E doesn't have a y component (its the same E from above), so Dn would be 0. Dt is also 0 correct? so overall, D would be 0.

 

[formulajoe]

if somebody can confirm my answers that would be great. i also have another one i need confirmation on.

A conducting sphere of radius a is half-embedded in a liquid dielectric medium of permittivity E1. The region above the liquid is a gas of permittivity E2. If the total free charge on the sphere is Q, determine the electric field intensity everywhere.

E inside the conductor is zero.

E at boundary with region 1 = (Q/surface area)/E1

E at boundary with region 2 = (Q/surface area)/E2

surface area = 4*pi*a^2

is there sometihng at the boundary between the two materials?
the only E is going to be normal to the sphere, so it would seem to me that the electric field would not be passing the boundary.

 

[Timbuqtu]

question 1: Seems correct to me, although the minus-sign is arbitrary (it depends on whether the field points toward or away from the conductor).

question 2: Unreadible

question 3: why do you think the surface charge (Q/surface area) is uniform on the whole sphere?

 

[formulajoe]

it doesn't not say the surface charge is not uniform. if its not uniform, than i don't see any way to solve it with the information I've been given.

Fixed Question 2

Region y is greater than or equal to 2 is occupied by a conductor. If the surface charge on the conductor is -20 nC/M^2, find D just outside the conductor.
Since the surface is y = 2, than the normal would be purely in the y direction. D = Eo*E. E doesn't have a y component (its the same E from above), so Dnormal would be 0. Dtangential is also 0 correct? so overall, D would be 0.

 

[formulajoe]

if the surface charge was not uniform, would the electric field be proportional to the permittivity of the medium?