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, wille neatly in straight lines; use equal signs. Good luck, YULILILIUJ LLIU TUULUIS, LAPPU where...
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...
4. Consider the dielectric slab shown below: The electric field within the slab is: E(T) =...
4. Consider the dielectric slab shown below: The electric field within the slab is: E(T) = 2 âz [V/m] and the susceptibility of the dielectric is 2.0, find: (a) the permittivity and relative permittivity of the dielectric. (b) the electric flux density within the slab. (c) the polarization vector within the slab. (d) the volume bound charge density within the slab. (e) the surface bound charge density at the top and bottom of the slab.
5. (20 points) For many dielectric materials, the relationship between the displacement field D a...
5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is...
An infinite line charge, with charge density p 10 (C/m), lies on the 2 axis. A...
An infinite line charge, with charge density p 10 (C/m), lies on the 2 axis. A nearby dielectric interface has the equation y = 2 (m). The < 2 region is free-space, while the y > 2 region has the relative permittivity of cr - 11. Find the electric field intensity, E. in all regions.
(1 point) Two different ideal dielectrics fill all of space. The relative permittivity in the region...
(1 point) Two different ideal dielectrics fill all of space. The relative permittivity in the region where 6x – 2y + 3z > 6 is eri = 3.5, while the relative permittivity everywhere else is Er2 = 1.5. In each dielectric region, the electric field intensity is constant. (Of course the constant for Region 1 need not be identical to the constant for Region 2.) Given the electric field intensity E(2,1,1) = (–70, 0, 42) V/m, find the electric flux...
3 Questions Find: a) The electric flux density vector: D=-EVV, where & is a constant =...
3 Questions Find: a) The electric flux density vector: D=-EVV, where & is a constant = 10 pF/m. b) The electric volume charge density at any point in the region: p, = V D= divergence ofD e) The total charge enclosed by the specified region: Q= fpdv, dv element of volume d) Find Vx D and show that D is irrotational. In the cylindrical region: 0srs2m, 0s0s7/2 0szslm, the potential field V is given by V=50 2 sin volts
3...
3 Questions Find a) The electric flux density vector: D-EVV, where s is a constant 10...
3 Questions Find a) The electric flux density vector: D-EVV, where s is a constant 10 pF/m. b) The electric volume charge density at any point in the region: p, = V. D = divergence of D c) The total charge enclosed by the specified region: Q ffp,dv, dv element of volume d) Find VxD and show that D is irrotational In the cylindrical region: 0srs2m, 0s0s7/2, 0szslm, the potential field Vis given by V=50 sin volts
3 Questions Find...
A spherical capacity consists of two metal shells made up of perfect conductors between which two...
A spherical capacity consists of two metal shells made up of perfect conductors between which two dielectric hemispheres of different permittivity are arranged. A voltage of V0 volts is applied to the outer metal shell while the inner shell is connected to ground (V = 0 volts)
a) Apply the Poisson equation to find the equation describing
the electrical potential in the structure
b) From your answer found in a), calculate the electric field in
the structure
c) Apply border...
Epsilon1=2 Epsilon0 6. In the spherical region #1 (0 r a, 0 θ π ,0 φ...
Epsilon1=2 Epsilon0
6. In the spherical region #1 (0 r a, 0 θ π ,0 φ 2π ), the electric field just below the spherical surface r-din region # i (where espe ) is given by E,,10+ 20 + ф40 . Gue On the spherical surface at r -a there exists a uniform surface charge density Pso 8 Find 52 in region #2 just above r a. Hint: Let E,EE+0E2,
electromagnetic (b) Use the expression obtained in part(a) to calculate the approximate capacitance of a a...
electromagnetic
(b) Use the expression obtained in part(a) to calculate the approximate capacitance of a a distance 2 mm. Perform this as a "back of the envelope" calculation by rounding 2) Ideal Parallel Plate Capacitor: (12 pts) (a) Starting with Gauss' Law, derive the capacitance of two oppositely charged finite sheets of surface charge density to and area A separated by a distance d. Assume that the electric field between the two sheets is constant (i.e. neglect fringe-effects) +o d...
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...
4. Consider the dielectric slab shown below: The electric field within the slab is: E(T) = 2 âz [V/m] and the susceptibility of the dielectric is 2.0, find: (a) the permittivity and relative permittivity of the dielectric. (b) the electric flux density within the slab. (c) the polarization vector within the slab. (d) the volume bound charge density within the slab. (e) the surface bound charge density at the top and bottom of the slab.
5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is...
An infinite line charge, with charge density p 10 (C/m), lies on the 2 axis. A nearby dielectric interface has the equation y = 2 (m). The < 2 region is free-space, while the y > 2 region has the relative permittivity of cr - 11. Find the electric field intensity, E. in all regions.
(1 point) Two different ideal dielectrics fill all of space. The relative permittivity in the region where 6x – 2y + 3z > 6 is eri = 3.5, while the relative permittivity everywhere else is Er2 = 1.5. In each dielectric region, the electric field intensity is constant. (Of course the constant for Region 1 need not be identical to the constant for Region 2.) Given the electric field intensity E(2,1,1) = (–70, 0, 42) V/m, find the electric flux...
3 Questions Find: a) The electric flux density vector: D=-EVV, where & is a constant = 10 pF/m. b) The electric volume charge density at any point in the region: p, = V D= divergence ofD e) The total charge enclosed by the specified region: Q= fpdv, dv element of volume d) Find Vx D and show that D is irrotational. In the cylindrical region: 0srs2m, 0s0s7/2 0szslm, the potential field V is given by V=50 2 sin volts
3...
3 Questions Find a) The electric flux density vector: D-EVV, where s is a constant 10 pF/m. b) The electric volume charge density at any point in the region: p, = V. D = divergence of D c) The total charge enclosed by the specified region: Q ffp,dv, dv element of volume d) Find VxD and show that D is irrotational In the cylindrical region: 0srs2m, 0s0s7/2, 0szslm, the potential field Vis given by V=50 sin volts
3 Questions Find...
A spherical capacity consists of two metal shells made up of perfect conductors between which two dielectric hemispheres of different permittivity are arranged. A voltage of V0 volts is applied to the outer metal shell while the inner shell is connected to ground (V = 0 volts)
a) Apply the Poisson equation to find the equation describing
the electrical potential in the structure
b) From your answer found in a), calculate the electric field in
the structure
c) Apply border...
Epsilon1=2 Epsilon0
6. In the spherical region #1 (0 r a, 0 θ π ,0 φ 2π ), the electric field just below the spherical surface r-din region # i (where espe ) is given by E,,10+ 20 + ф40 . Gue On the spherical surface at r -a there exists a uniform surface charge density Pso 8 Find 52 in region #2 just above r a. Hint: Let E,EE+0E2,
electromagnetic
(b) Use the expression obtained in part(a) to calculate the approximate capacitance of a a distance 2 mm. Perform this as a "back of the envelope" calculation by rounding 2) Ideal Parallel Plate Capacitor: (12 pts) (a) Starting with Gauss' Law, derive the capacitance of two oppositely charged finite sheets of surface charge density to and area A separated by a distance d. Assume that the electric field between the two sheets is constant (i.e. neglect fringe-effects) +o d...
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