Homework Answers
a) In a certain region, u 5 sin 210 t a, A/m. Find the rate of...
a) In a certain region, u 5 sin 210 t a, A/m. Find the rate of change of flux over the surface of 20 m2 2Ho, 3E0, the magnetic field intensity is given as H = E= b) In a certain region, J (za-4yaytxa) Find py if pv (x, 0, z, t) 0 cos wt A/m2 Solution:
Please show the solutions for all 4 parts! Problem 1 Let m E Z that is...
Please show the solutions for all 4 parts!
Problem 1 Let m E Z that is not the square of an integer (ie. mメ0, 1.4.9, ). Let α-Vm (so you have a失Q as mentioned above) (i) Prove the following:Qla aba: a,b Q is a subring of C, Za]a +ba: a, b E Z is a subring of Qla], and the fraction field of Z[a] is Q[a]. (3pts) (ii) Prove that Z[x]/(X2-m) Z[a] and Qx/(x2 mQ[a]. (3pts) i Let n be...
A cubical region 1.0 m on a side is located between x = 0 and x...
A cubical region 1.0 m on a side is located between x = 0 and x = 1 m. The region contains an electric field whose magnitude varies with x but is independent of y and z: E = E_0(x/x_0), where E_0 = 16 kV/m and x_0 = 7.0 m. Find the total energy in the region. Express your answer using two significant figures. U =
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (...
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (a·y) E R2 Prove that:
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2...
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...
1. Let h be a hash function mapping U to indexes (0...m -1]. Assume that |U|...
1. Let h be a hash function mapping U to indexes (0...m -1]. Assume that |U| m2 Could an adversary could pick a set K of m/2 keys from U which are all mapped into the same cell? What is the value of ΣzyEKFh(x,y) in this case ? Fh(x,y) is the function defined in the slides on the section discussing Universal Families of Hash functions.
with in a certain region =10-11 F/m and u=10-5 H/m if Bx= T (a) use to...
with in a certain region
=10-11 F/m and u=10-5 H/m if Bx=
T (a) use
to find E (b) find the total magnetic flux passing through the
surface x=0 0<y<40m, 0<z<2m at t= 1us (c) find the
value of the closed line integral of E around the perimiter of
given surface.
please solve neatly with proper explanation of each step
We were unable to transcribe this image2 * 10-4 cos 10°tsin 10-33 / We were unable to transcribe this image
1. Consider a fictitious cube region with dimension (1 m) (1 m)x(1 m). It is anchored...
1. Consider a fictitious cube region with dimension (1 m) (1 m)x(1 m). It is anchored at the spatial origin and point (1,1,1) m. All of its faces are parallel to the Cartesian axes, as shown in the figure below. Suppose a static vector field exists in the space, A(x, y, z) = x2 yzî + xy2 zý + xyz22. Please verify the Gauss's theorem, SS V. Adv = ffA.ds, where V is the cube region and S is the...
1. Let E be the solid region bounded above by the sphere 4 = x2 +...
1. Let E be the solid region bounded above by the sphere 4 = x2 + y2 + z2 and below by the plane y-z =-2. a. Generate a 3D picture of the region E using 3D graphing software. b. Write the integral J [ f(x,y,z)dVas an iterated integral (in rectangular coordinates) in two different ways - one with integration with respect to z first, and one with integration with respect to y first.
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the fi...
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the figure below. The inner conductor has a radius of R1 = 1.00cm. The outer conductor has a radius R2 = 2.00cm and has negligible thickness. The inner conductor has a current density given by J 2.00A p (TR1) flowing out of the page (positive z direction), where ρ is the radial direction. The outer conductor has a current 1 of 1.00 Amperes...
a) In a certain region, u 5 sin 210 t a, A/m. Find the rate of change of flux over the surface of 20 m2 2Ho, 3E0, the magnetic field intensity is given as H = E= b) In a certain region, J (za-4yaytxa) Find py if pv (x, 0, z, t) 0 cos wt A/m2 Solution:
Please show the solutions for all 4 parts!
Problem 1 Let m E Z that is not the square of an integer (ie. mメ0, 1.4.9, ). Let α-Vm (so you have a失Q as mentioned above) (i) Prove the following:Qla aba: a,b Q is a subring of C, Za]a +ba: a, b E Z is a subring of Qla], and the fraction field of Z[a] is Q[a]. (3pts) (ii) Prove that Z[x]/(X2-m) Z[a] and Qx/(x2 mQ[a]. (3pts) i Let n be...
A cubical region 1.0 m on a side is located between x = 0 and x = 1 m. The region contains an electric field whose magnitude varies with x but is independent of y and z: E = E_0(x/x_0), where E_0 = 16 kV/m and x_0 = 7.0 m. Find the total energy in the region. Express your answer using two significant figures. U =
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2 If(x,y)| 〈 M(x2 + y2)· for all (a·y) E R2 Prove that:
1(a) Let f : R2 → R b constant M > 0 such that livf(x,y)|| (0.0)-0. Assume that there exists a e continuously differentiable, with Mv/r2 + уг, for all (z. y) E R2...
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...
1. Let h be a hash function mapping U to indexes (0...m -1]. Assume that |U| m2 Could an adversary could pick a set K of m/2 keys from U which are all mapped into the same cell? What is the value of ΣzyEKFh(x,y) in this case ? Fh(x,y) is the function defined in the slides on the section discussing Universal Families of Hash functions.
with in a certain region
=10-11 F/m and u=10-5 H/m if Bx=
T (a) use
to find E (b) find the total magnetic flux passing through the
surface x=0 0<y<40m, 0<z<2m at t= 1us (c) find the
value of the closed line integral of E around the perimiter of
given surface.
please solve neatly with proper explanation of each step
We were unable to transcribe this image2 * 10-4 cos 10°tsin 10-33 / We were unable to transcribe this image
1. Consider a fictitious cube region with dimension (1 m) (1 m)x(1 m). It is anchored at the spatial origin and point (1,1,1) m. All of its faces are parallel to the Cartesian axes, as shown in the figure below. Suppose a static vector field exists in the space, A(x, y, z) = x2 yzî + xy2 zý + xyz22. Please verify the Gauss's theorem, SS V. Adv = ffA.ds, where V is the cube region and S is the...
1. Let E be the solid region bounded above by the sphere 4 = x2 + y2 + z2 and below by the plane y-z =-2. a. Generate a 3D picture of the region E using 3D graphing software. b. Write the integral J [ f(x,y,z)dVas an iterated integral (in rectangular coordinates) in two different ways - one with integration with respect to z first, and one with integration with respect to y first.
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the figure below. The inner conductor has a radius of R1 = 1.00cm. The outer conductor has a radius R2 = 2.00cm and has negligible thickness. The inner conductor has a current density given by J 2.00A p (TR1) flowing out of the page (positive z direction), where ρ is the radial direction. The outer conductor has a current 1 of 1.00 Amperes...
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