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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 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...
1Introduction Computer equipments, x-ray machines, medical diagnosis equipments and many other industrial equipment are designed using...
1Introduction Computer equipments, x-ray machines, medical diagnosis equipments and many other industrial equipment are designed using electrostatic field theory. The theory uses essential mathematical tools such Since real life engineering applications involve 3D geometries whose fields are as vector calculus. functions of space (and time), it is critical that you master these tools. In real life, equipment/devices are not restricted to rectangular/cubical geometries but may be of cylindrical/spherical shapes. Objective: For a given scalar potential distribution inside a region, it...
Please step by step for D(electric flux density), E(electric field), V(electric potantial), P(polarization vector) ? A...
Please step by step for
D(electric flux density), E(electric field), V(electric potantial),
P(polarization vector) ?
A positive point charge Q is at the center of a spherical dielectric shell of an inner radius Ri and an outer radius RO. Determine E, V, D, and P as functions of the radial distance R. a)R>RO b)Ri<R<RO c)R<R find it. E1 = 60 €2 = Erzo (E3 = 6,360 = 0 - R + Ro conductive dielectric dielectric
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE A. The component of flux, given flux density F,...
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE
A. The component of flux, given flux density F, crossing the surface dsu F.ûdsu OB. In spherical coordinates the following is true for any point, r= Rsin o cos 6î + Rsin o sin oſ + R cos and de =R c. The gradient in the u, v, w coordinates is 1 0 1 0 V= ü+T V .hu du h, du + 1 0 hw dw Then, the component of flux, given...
(i) Electric flux froin volume Vis given by the surface integral of electric field E: where...
(i) Electric flux froin volume Vis given by the surface integral of electric field E: where S is the outer surface of volume V and η is a unit vector normal to surface S. Find the total flux of the electric field E = [y2, 0,23] from the charged cylinder desribed by s4, 0 sz s 5 where surface S comprises the top, base and curved side of the cylinder. [10 marka] (ii) Use Gauss's divergence theorem to verify your...
If a vector field is defined as A = 5x 2(sinmx)a x, find div (A) for x-1. The density given by the density of ps 12...
If a vector field is defined as A = 5x 2(sinmx)a x, find div (A) for x-1. The density given by the density of ps 12 sin ø uC/m2, with 4 m radius circular disc shaped charge distribution is surrounded by S surface. What is the net flux that cuts S surface? Expression of a vector field in cylindrical coordinates is given by Zre-sza z Determine div(A) at (1 /2, π / 2,0)
If a vector field is defined as...
Problem #4: F.ndS Use the divergence theorem find the outward flux of the field to vector...
Problem #4: F.ndS Use the divergence theorem find the outward flux of the field to vector e+7 cosxj +y? and x2 + y2 V 49 an (3y + 8z) i 2 2 k, where S is the surface of the region bounded by the F graphs of z Vx V + symbolically, Enter your answer (sqrt(2)-1)*(686/3*pi) as in these examples Problem #4 686 JT 3 Submit Problem # 4 for Grading Just Save Attempt #3 Problem #4 Attempt #1 Attempt...
Problem A.1 - Calculate electric flux f5) The electric field due to an infinite line of...
Problem A.1 - Calculate electric flux f5) The electric field due to an infinite line of charge is perpendicular to the line and has magnitude E . Consider an imaginary cylinder with radius e-25 cm and length L = 40 cm that has an infinite line of positive charge running along its axis. The charge per unit length is 3 HC/m. Do not use Gauss's Law, but actually calculate the flux! a) What is the electric flux through the cylinder...
1. Find the electric field at point a for: a. A solid sphere of radius R...
1. Find the electric field at point a for: a. A solid sphere of radius R carrying a volume charge density ρ b. An infinitely long, thin wire carrying a line charge density Side Cross Section C. A plane of infinite area carrying a surface charge density ơ PoT 2. Avery long cylinder with radius a and charge density pa-is placed inside of a conducting cylindrical shell. The cylindrical shell has an inner radius of b and a thickness of...
4. Consider the vector field u = (3r+yz) region V bounded by 2y2 < (2 -...
4. Consider the vector field u = (3r+yz) region V bounded by 2y2 < (2 - z)2 for y 2 0 and 0 y)j+(xy+2z)k, defined across a three-dimensional 1. z (a) Show that u is conservative and find a scalar function d that satisfies u = Vo. [6 marks] (b) Sketch the volume V and express the limits of the volume V in terms of cylindrical coordi nates (r, 0, z) [3 marks (c) Using the divergence theorem calculate the...
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...
1Introduction Computer equipments, x-ray machines, medical diagnosis equipments and many other industrial equipment are designed using electrostatic field theory. The theory uses essential mathematical tools such Since real life engineering applications involve 3D geometries whose fields are as vector calculus. functions of space (and time), it is critical that you master these tools. In real life, equipment/devices are not restricted to rectangular/cubical geometries but may be of cylindrical/spherical shapes. Objective: For a given scalar potential distribution inside a region, it...
Please step by step for
D(electric flux density), E(electric field), V(electric potantial),
P(polarization vector) ?
A positive point charge Q is at the center of a spherical dielectric shell of an inner radius Ri and an outer radius RO. Determine E, V, D, and P as functions of the radial distance R. a)R>RO b)Ri<R<RO c)R<R find it. E1 = 60 €2 = Erzo (E3 = 6,360 = 0 - R + Ro conductive dielectric dielectric
MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE
A. The component of flux, given flux density F, crossing the surface dsu F.ûdsu OB. In spherical coordinates the following is true for any point, r= Rsin o cos 6î + Rsin o sin oſ + R cos and de =R c. The gradient in the u, v, w coordinates is 1 0 1 0 V= ü+T V .hu du h, du + 1 0 hw dw Then, the component of flux, given...
(i) Electric flux froin volume Vis given by the surface integral of electric field E: where S is the outer surface of volume V and η is a unit vector normal to surface S. Find the total flux of the electric field E = [y2, 0,23] from the charged cylinder desribed by s4, 0 sz s 5 where surface S comprises the top, base and curved side of the cylinder. [10 marka] (ii) Use Gauss's divergence theorem to verify your...
If a vector field is defined as A = 5x 2(sinmx)a x, find div (A) for x-1. The density given by the density of ps 12 sin ø uC/m2, with 4 m radius circular disc shaped charge distribution is surrounded by S surface. What is the net flux that cuts S surface? Expression of a vector field in cylindrical coordinates is given by Zre-sza z Determine div(A) at (1 /2, π / 2,0)
If a vector field is defined as...
Problem #4: F.ndS Use the divergence theorem find the outward flux of the field to vector e+7 cosxj +y? and x2 + y2 V 49 an (3y + 8z) i 2 2 k, where S is the surface of the region bounded by the F graphs of z Vx V + symbolically, Enter your answer (sqrt(2)-1)*(686/3*pi) as in these examples Problem #4 686 JT 3 Submit Problem # 4 for Grading Just Save Attempt #3 Problem #4 Attempt #1 Attempt...
Problem A.1 - Calculate electric flux f5) The electric field due to an infinite line of charge is perpendicular to the line and has magnitude E . Consider an imaginary cylinder with radius e-25 cm and length L = 40 cm that has an infinite line of positive charge running along its axis. The charge per unit length is 3 HC/m. Do not use Gauss's Law, but actually calculate the flux! a) What is the electric flux through the cylinder...
1. Find the electric field at point a for: a. A solid sphere of radius R carrying a volume charge density ρ b. An infinitely long, thin wire carrying a line charge density Side Cross Section C. A plane of infinite area carrying a surface charge density ơ PoT 2. Avery long cylinder with radius a and charge density pa-is placed inside of a conducting cylindrical shell. The cylindrical shell has an inner radius of b and a thickness of...
4. Consider the vector field u = (3r+yz) region V bounded by 2y2 < (2 - z)2 for y 2 0 and 0 y)j+(xy+2z)k, defined across a three-dimensional 1. z (a) Show that u is conservative and find a scalar function d that satisfies u = Vo. [6 marks] (b) Sketch the volume V and express the limits of the volume V in terms of cylindrical coordi nates (r, 0, z) [3 marks (c) Using the divergence theorem calculate the...
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