hard_revenge
11-12-2006, 02:43 AM
السلام عليكم ورحمه الله وبركاته الى المسائل
المجموعه الخامسه
A planar capacitor is made of two parallel plates each of area S separated by a two layer dielectric. The lower layer is of thickness d1 and permittivity ε1 and the upper of thickness d2 and permittivity ε2. The upper plate is at voltage V and the lower at voltage 0. Find the voltage and electric field distributions and the capacitance between the plates. (Solve Laplace’s equation in the two layers and notice that the potential is continuous across the interface between them.)
The inner conductor radius of a coaxial line is a and the inner radius of its outer conductor is b. The inner conductor is coated with a dielectric layer of thickness t and permittivity ε1. The permittivity of the remaining space between conductors is ε2. The inner conductor is at voltage V and the outer is earthed. Determine the charge density on the inner conductor and the capacitance per unit length.
The conducting spherical surfaces r = 3 and r = 6 cm are at potentials 10V and 0V, respectively. The region 3 <r< 4 is filled with a dielectric ε and the region 4 <r< 6 is air. Determine the charge density on the inner and outer spheres and the capacitance between them.
A potential field V = 40x – 20y + 35z + 10 kV exists between two parallel conducting plates, each having an area 12000 mm2. The plates are separated by 8 mm. If the medium between the plates is air, find the voltage between the plates, the charge density on each plate and the capacitance between them.
Two square conducting plates 0.50 m on a side are separated by 0.02 m along one side and 0.25 m along the other so that the two plates are not parallel but inclined to each other. The space between the plates is filled with a dielectric ε. Assume a voltage difference and find the capacitance.
An uncharged ****l sphere of radius R is placed in an otherwise uniform electric field. The center of the sphere is at the origin and the uniform field is along the z axis, i.e. E = Eo az. Verify that the potential outside the sphere is of the form V = (Ar + B/r2) cos θ. Find the constants A and B to satisfy the boundary conditions at r =R and at infinity.
A uniform line charge ρ C/m is placed on an infinite straight wire parallel to the x axis and a distance d above a conducting grounded plane. Find the potential above the conducting plane and the surface charge density induced on the plane.
A grounded conducting solid cylinder has a radius a. The axis of the cylinder is the z axis. A thin wire is parallel to the z axis through the point x = d >a, y = 0. The wire carries a uniform charge ρ C/m. What is the image of the line charge into the cylinder? Use this image to find the potential and electric field outside the cylinder in Cartesian coordinates
In spherical coordinates, the perfectly conducting cone θ = 30o has its vertex separated from the grounded conducting plane θ = 90o by an infinitesimal insulating gap. If the cone is at potential 100 V, find the electric field at the point r = 2, θ = 60o. If the cone is of height 1m, determine the capacitance between it and the earth.
In cylindrical coordinates, the surfaces r = a and r = b are equipotentials with potential U and 0, respectively. The space between the two surfaces is filled with a charge of uniform density q C/m3. Use Poisson’s equation to find the potential and electric field distributions.
المجموعه السادسه
An infinitly long filament on the x axis carries a current of 10 mA in the x-direcion. Find the magnetic field H at the point (3,4,2).
A surface current of denssity Js = 4r aφ A/m flows in the z = 0 plane within the annular region 2 < r< 5 m. What current does cross the φ = 0 plane? Find H at the point (0,0,d). (Note: Cylindrical coordinates are used.)
Find H at the origin for the current sheet Js on the cylinder r = a in the two cases: a) Js = Jo aφ A/m and b) Js = Jo az A/m.
The region 0 < x< 6m carries the uniform volume charge density Jv = 5 az A/m2 and Jv = 0 elsewhere. Use Ampere’s circuital law and rectangular paths in the z = 0 plane to show that Hx<0 = - Hx>6 and hence find H at the points (8,9,0) and (2,5,0).
Given the magnetic field H = [ 1/r – (40 + r-1) exp(-40r) ] aφ A/m, in cylindrical coordinates, find the magnetic field H and the volume current density J at the origin. Find the total current flowing within the cylinder r = 1 cm by two different methods.
Two infinite slabs of homogeneous, linear, isotropic magnetic materials are located in free space perpenicular to the z axis. The lower one has μr = 5 and occupies the region 0<z<4mm. The upper slab has μr = 2 and occupies the region 4<z<7mm. If the magnetic field inside the lower slab is H = ax – 2ay + 3az kA/m, find the field H inside the upper slab and in the free space above it and the angle which H makes with the z axis in each region. Determine B and M in all regions.
Find H, B, and M everywhere if J = 3az kA/m2 and μr = 5 within the region –0.1 < y < +0.2 m, while J = 0 and μr = 1.5 elsewhere.
An electron starts motion at the origin with a speed vo = 106(3ax + 4ay) m/sec.A uniform magnetic field parallel to the y axis and with flux density 5.0 mWb/m2 exists in the region. Describe the electron trajectory through the field. Find the position of the electron in space at t = 5 nsec after the start. What would be the answer if an electric field E = 20 ay kV/m were present?
An infinite solenoid has N turns per unit length, radius R, and current I. Apply Ampere’s law to appropriate amperian loops to show that B = μoNI az inside the solenoid and B = 0 outside the solenoid. Verify that the vector magnetic potential is given by: A = μoNI r /2 aφ r < R, A = μoNI R2 /2r aφ r > R.
Two long coaxial solenoids have as common axis the z axis. The inner one has N1 turns per meter and the outer has N2 turns pe rmeter. Find H everywhere for the two cases: a) the currents in the two solenoids are equal and opposite, and b) the currents are equal and in the same direction.
Find the magnetic field H produced by an infinite uniform surface current Js A/m covering the xy plane.
A thick slab extends from -¥ < x < ¥, -¥ < y < ¥, and -a/2 < z < a/2 carries a uniform volume current density J = Jo ax A/m2. Find H both inside and outside the slab. [Hint: make use of the result of problem 11.]
وطبعا هذا ليس اخر مجموعه ولكن هناك تقريبا واحده او اتنين ربما ثلاثه لعلما اربعه قد تكون خمسه ان شاء الله جايه فى الطريق بس معلش لسه موصلتش وشكرا سلاموز
المجموعه الخامسه
A planar capacitor is made of two parallel plates each of area S separated by a two layer dielectric. The lower layer is of thickness d1 and permittivity ε1 and the upper of thickness d2 and permittivity ε2. The upper plate is at voltage V and the lower at voltage 0. Find the voltage and electric field distributions and the capacitance between the plates. (Solve Laplace’s equation in the two layers and notice that the potential is continuous across the interface between them.)
The inner conductor radius of a coaxial line is a and the inner radius of its outer conductor is b. The inner conductor is coated with a dielectric layer of thickness t and permittivity ε1. The permittivity of the remaining space between conductors is ε2. The inner conductor is at voltage V and the outer is earthed. Determine the charge density on the inner conductor and the capacitance per unit length.
The conducting spherical surfaces r = 3 and r = 6 cm are at potentials 10V and 0V, respectively. The region 3 <r< 4 is filled with a dielectric ε and the region 4 <r< 6 is air. Determine the charge density on the inner and outer spheres and the capacitance between them.
A potential field V = 40x – 20y + 35z + 10 kV exists between two parallel conducting plates, each having an area 12000 mm2. The plates are separated by 8 mm. If the medium between the plates is air, find the voltage between the plates, the charge density on each plate and the capacitance between them.
Two square conducting plates 0.50 m on a side are separated by 0.02 m along one side and 0.25 m along the other so that the two plates are not parallel but inclined to each other. The space between the plates is filled with a dielectric ε. Assume a voltage difference and find the capacitance.
An uncharged ****l sphere of radius R is placed in an otherwise uniform electric field. The center of the sphere is at the origin and the uniform field is along the z axis, i.e. E = Eo az. Verify that the potential outside the sphere is of the form V = (Ar + B/r2) cos θ. Find the constants A and B to satisfy the boundary conditions at r =R and at infinity.
A uniform line charge ρ C/m is placed on an infinite straight wire parallel to the x axis and a distance d above a conducting grounded plane. Find the potential above the conducting plane and the surface charge density induced on the plane.
A grounded conducting solid cylinder has a radius a. The axis of the cylinder is the z axis. A thin wire is parallel to the z axis through the point x = d >a, y = 0. The wire carries a uniform charge ρ C/m. What is the image of the line charge into the cylinder? Use this image to find the potential and electric field outside the cylinder in Cartesian coordinates
In spherical coordinates, the perfectly conducting cone θ = 30o has its vertex separated from the grounded conducting plane θ = 90o by an infinitesimal insulating gap. If the cone is at potential 100 V, find the electric field at the point r = 2, θ = 60o. If the cone is of height 1m, determine the capacitance between it and the earth.
In cylindrical coordinates, the surfaces r = a and r = b are equipotentials with potential U and 0, respectively. The space between the two surfaces is filled with a charge of uniform density q C/m3. Use Poisson’s equation to find the potential and electric field distributions.
المجموعه السادسه
An infinitly long filament on the x axis carries a current of 10 mA in the x-direcion. Find the magnetic field H at the point (3,4,2).
A surface current of denssity Js = 4r aφ A/m flows in the z = 0 plane within the annular region 2 < r< 5 m. What current does cross the φ = 0 plane? Find H at the point (0,0,d). (Note: Cylindrical coordinates are used.)
Find H at the origin for the current sheet Js on the cylinder r = a in the two cases: a) Js = Jo aφ A/m and b) Js = Jo az A/m.
The region 0 < x< 6m carries the uniform volume charge density Jv = 5 az A/m2 and Jv = 0 elsewhere. Use Ampere’s circuital law and rectangular paths in the z = 0 plane to show that Hx<0 = - Hx>6 and hence find H at the points (8,9,0) and (2,5,0).
Given the magnetic field H = [ 1/r – (40 + r-1) exp(-40r) ] aφ A/m, in cylindrical coordinates, find the magnetic field H and the volume current density J at the origin. Find the total current flowing within the cylinder r = 1 cm by two different methods.
Two infinite slabs of homogeneous, linear, isotropic magnetic materials are located in free space perpenicular to the z axis. The lower one has μr = 5 and occupies the region 0<z<4mm. The upper slab has μr = 2 and occupies the region 4<z<7mm. If the magnetic field inside the lower slab is H = ax – 2ay + 3az kA/m, find the field H inside the upper slab and in the free space above it and the angle which H makes with the z axis in each region. Determine B and M in all regions.
Find H, B, and M everywhere if J = 3az kA/m2 and μr = 5 within the region –0.1 < y < +0.2 m, while J = 0 and μr = 1.5 elsewhere.
An electron starts motion at the origin with a speed vo = 106(3ax + 4ay) m/sec.A uniform magnetic field parallel to the y axis and with flux density 5.0 mWb/m2 exists in the region. Describe the electron trajectory through the field. Find the position of the electron in space at t = 5 nsec after the start. What would be the answer if an electric field E = 20 ay kV/m were present?
An infinite solenoid has N turns per unit length, radius R, and current I. Apply Ampere’s law to appropriate amperian loops to show that B = μoNI az inside the solenoid and B = 0 outside the solenoid. Verify that the vector magnetic potential is given by: A = μoNI r /2 aφ r < R, A = μoNI R2 /2r aφ r > R.
Two long coaxial solenoids have as common axis the z axis. The inner one has N1 turns per meter and the outer has N2 turns pe rmeter. Find H everywhere for the two cases: a) the currents in the two solenoids are equal and opposite, and b) the currents are equal and in the same direction.
Find the magnetic field H produced by an infinite uniform surface current Js A/m covering the xy plane.
A thick slab extends from -¥ < x < ¥, -¥ < y < ¥, and -a/2 < z < a/2 carries a uniform volume current density J = Jo ax A/m2. Find H both inside and outside the slab. [Hint: make use of the result of problem 11.]
وطبعا هذا ليس اخر مجموعه ولكن هناك تقريبا واحده او اتنين ربما ثلاثه لعلما اربعه قد تكون خمسه ان شاء الله جايه فى الطريق بس معلش لسه موصلتش وشكرا سلاموز