- #1
Bugge
- 10
- 1
Hello. I have DC going through a coaxial cable, and I have calculated the E fields of the two dielectrics in between to be [itex]E_1[/itex] and [itex]E_2[/itex] with help of their [itex]D[/itex]-vectors. The dielectrics are cylindrically shaped like the conductors. As in, one is in contact with the inner conductor, and one is in contact with the outer.
Both fields vary by the distance [itex]r[/itex] through the [itex]D[/itex]-fields,
[tex]a < r < c[/tex]
[tex]c < r < b[/tex]
Where [itex]a[/itex] is the inner conductor radius and [itex]b[/itex] is the outer conductor radius, and [itex]c[/itex] is inbetween the dielectrics.
Now I am not sure how to determine the potential. between them. Considering the different E-fields, how is,
[tex]V(r) = \int_b^a E d \mathcal{l}[/tex]
expressed in my case? Would it be similar to
[tex]\int_a^b (E_2 - E_1) dr = \int_a^b E_2 dr - \int_a^b E_1 dr[/tex]I know the [itex]E_n[/itex]-fields, and [itex]J_n[/itex]- and [itex]D_n[/itex]-vectors of the dielectrics. I also know the [itex]\sigma_n[/itex] of each of the dielectrics and the surface charge density of the inner ([itex]\rho_si[/itex]) conductor and there is also a [itex]\rho_sc[/itex] between the dielectrics at distance [itex]c[/itex].
I'd appreciate any help, thank you very much!
Both fields vary by the distance [itex]r[/itex] through the [itex]D[/itex]-fields,
[tex]a < r < c[/tex]
[tex]c < r < b[/tex]
Where [itex]a[/itex] is the inner conductor radius and [itex]b[/itex] is the outer conductor radius, and [itex]c[/itex] is inbetween the dielectrics.
Now I am not sure how to determine the potential. between them. Considering the different E-fields, how is,
[tex]V(r) = \int_b^a E d \mathcal{l}[/tex]
expressed in my case? Would it be similar to
[tex]\int_a^b (E_2 - E_1) dr = \int_a^b E_2 dr - \int_a^b E_1 dr[/tex]I know the [itex]E_n[/itex]-fields, and [itex]J_n[/itex]- and [itex]D_n[/itex]-vectors of the dielectrics. I also know the [itex]\sigma_n[/itex] of each of the dielectrics and the surface charge density of the inner ([itex]\rho_si[/itex]) conductor and there is also a [itex]\rho_sc[/itex] between the dielectrics at distance [itex]c[/itex].
I'd appreciate any help, thank you very much!