Find the boundary conditions of the electric field in the normal direction and tangential direction at...
Find the boundary conditions of the electric field in the normal
direction and tangential direction at the interface consisting of
two dielectrics whose permittivity is ε1 and ε2, respectively.
(20)
In this case, tan (α1) / tan (α2) = ε1 / ε2 is satisfied when the
angles between the vertical lines of the interface and the electric
fields E1 and E2 are α1 and α2,
Homework Answers
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Find the boundary conditions of the electric field in the normal
direction and tangential direction at...
1. (10 pts) Electrostatic boundary conditions. The boundary between two dielectric materials with...
Electrostatic Boundary Conditions
1. (10 pts) Electrostatic boundary conditions. The boundary between two dielectric materials with relative permittivities of Er-3 and Er | 1s the y--x plane. El and E, are electric fields at the boundary and inside materials1 and 2, respectively. E21 Material 2 62=1 Material1 (a) Find E2 if E, 37 and there is no free surface charge on the boundary between the two materials (b) Find Eland E, if the x-component of E! is 1V/m, the y-component...
Electric fields are quantities whose magnitudes are measured in units volts/meter (v/m). Find resultant electric field...
Electric fields are quantities whose magnitudes are measured in units volts/meter (v/m). Find resultant electric field when there are 2 fields, E1 & E2. Where E1 is directed vertically upward and has magnitude of 109 v/m and E2 is directed 42 degrees left of E1 with magnitude 152 v/m. Magnitude? Direction ______ left of vertically up?
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the...
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the resultant electric field when there are two fields, E1 and E2, where E1 is directed vertically upward and has magnitude 98 V/m and E2 is directed 44° to the left of E1 and has magnitude 137 V/m. magnitude direction
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the...
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the resultant electric field when there are two fields, E1 and E2, where E1 is directed vertically upward and has magnitude 97 V/m and E2 is directed 44° to the left of E1 and has magnitude 157 V/m. magnitude direction left of vertically up
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the...
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the resultant electric field when there are two fields, E1 and E2, where E1 is directed vertically upward and has magnitude 106 V/m and E2 is directed 47° to the left of E1 and has magnitude 136 V/m magnitude direction left of vertically up
TM waves. For the case of an incident electric field incidence show that the boundary conditions (the parallel components of E and B/u are the same at both sides of the interface) leads to: E, parall...
TM waves. For the case of an incident electric field incidence show that the boundary conditions (the parallel components of E and B/u are the same at both sides of the interface) leads to: E, parallel to the plane of 4. n Cos lo and 2n Cos θ io οι OS
TM waves. For the case of an incident electric field incidence show that the boundary conditions (the parallel components of E and B/u are the same at both sides...
(1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two laye ers of dielectrics, di and de thick, with permittivities s and s2, respectively. Ignoring the r...
(1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two laye ers of dielectrics, di and de thick, with permittivities s and s2, respectively. Ignoring the ringe effect at the four edges (assuming rectangular plates), find the fields Ei and E2 in the t dielectric ctrics if a voltage V(assumed positive) is applied to the top plate with regard to the bottom plate. (Note: both magnitudes and directions needed.) (2) Find the...
Answer number 2 using the given hints. Thanks 1. For the given capacitor, there are conducting...
Answer number 2 using the given hints. Thanks
1. For the given capacitor, there are conducting plates at z = 0 and 2 = 3d. Between the plates, there are 3 layers of insulators: 2 free space regions and one dielectric with permittivity e. The electric field in Region 1 is E = - a, (V/m), where Ps is the surface charge density on the top plate ( = 30). The surface area of each plate is A. (a) What...
mainly just looking for clarification of part c) a= cos theta t / cos theta i , b=sin theta i/ sin theta t 5. A plane electrom netic wave is obliquely incident upon an infinite plane boundary two die...
mainly just looking for clarification of part c)
a= cos theta t / cos theta i , b=sin theta i/ sin theta t
5. A plane electrom netic wave is obliquely incident upon an infinite plane boundary two dielectrics with refractive indices, permittivities and permeabilities m. ει, μι and respectively. In terms of the angles of incidence, O, and refraction, e, define n2-E2, μ2 sin θ sin6, (a) State succinctly what assumptions have been made about the materials to write...
Wave Guide: Find an electric field that is a traveling wave and matches the boundary conditions of a wave guide. Show th...
Wave Guide: Find an electric field that is a traveling wave and matches the boundary conditions of a wave guide. Show that the wave number could be imaginary (and explain why this leads to a reasonable result!) or show that the velocity is greater than the velocity of light.
Electrostatic Boundary Conditions
1. (10 pts) Electrostatic boundary conditions. The boundary between two dielectric materials with relative permittivities of Er-3 and Er | 1s the y--x plane. El and E, are electric fields at the boundary and inside materials1 and 2, respectively. E21 Material 2 62=1 Material1 (a) Find E2 if E, 37 and there is no free surface charge on the boundary between the two materials (b) Find Eland E, if the x-component of E! is 1V/m, the y-component...
Electric fields are vector quantities whose magnitudes are measured in units of volts/meter (V/m). Find the resultant electric field when there are two fields, E1 and E2, where E1 is directed vertically upward and has magnitude 106 V/m and E2 is directed 47° to the left of E1 and has magnitude 136 V/m magnitude direction left of vertically up
TM waves. For the case of an incident electric field incidence show that the boundary conditions (the parallel components of E and B/u are the same at both sides of the interface) leads to: E, parallel to the plane of 4. n Cos lo and 2n Cos θ io οι OS
TM waves. For the case of an incident electric field incidence show that the boundary conditions (the parallel components of E and B/u are the same at both sides...
(1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two laye ers of dielectrics, di and de thick, with permittivities s and s2, respectively. Ignoring the ringe effect at the four edges (assuming rectangular plates), find the fields Ei and E2 in the t dielectric ctrics if a voltage V(assumed positive) is applied to the top plate with regard to the bottom plate. (Note: both magnitudes and directions needed.) (2) Find the...
Answer number 2 using the given hints. Thanks
1. For the given capacitor, there are conducting plates at z = 0 and 2 = 3d. Between the plates, there are 3 layers of insulators: 2 free space regions and one dielectric with permittivity e. The electric field in Region 1 is E = - a, (V/m), where Ps is the surface charge density on the top plate ( = 30). The surface area of each plate is A. (a) What...
mainly just looking for clarification of part c)
a= cos theta t / cos theta i , b=sin theta i/ sin theta t
5. A plane electrom netic wave is obliquely incident upon an infinite plane boundary two dielectrics with refractive indices, permittivities and permeabilities m. ει, μι and respectively. In terms of the angles of incidence, O, and refraction, e, define n2-E2, μ2 sin θ sin6, (a) State succinctly what assumptions have been made about the materials to write...
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