Q4/ Find the flux of (D= zx + xy - 3y'z z") out of a closed surface consistingof(1) the cylinder x' +y? =4 between z= 0 and z =2;(2) the circular area with radius(r = 2) which bounds the cylinder at z = 0;(3) the corresponding circular area at z = 2. The surface is shown in theaccompanying figure.Q5/Given A = e*x* +2cosyy + 2sinz", find V. A at the origin.Q6/ Show that the divergence of E is zero if E= (100/r)0+ 40z.Q7/ The region R < 2m (spherical coordinates) has a field E = (5R.10 /e0)R(V/m). Find the net charge enclosed by the shell R= 2m.Q8/ Given that D = (5R/4)R in spherical coordinates, evaluate both sides of%3D%3Dthe divergence theorem for the volume enclosed between R = 1 and R = 2.Q9/ Given that D = 10sinor*+ 2cos00" , evaluate both sides of the divergencetheorem for the volume enclosed by the shell r = 2.Q10/ Given that D = (10r'/4)r in cylindrical coordinates, evaluate both sidesof the divergence theorem for the volume enclosed by r = 2, z = 0, and z = 10.Q11/In a certain region, the electric field is given byD = 2r(z + I)cosOr^ - r(z + 1)sin00° +r°cosOz^ µC/m?(a) Find the charge density(b) Calculate the total charge enclosed by the volume 0

By bartleby rules, only 1,2,3 have been answered Given surface is D=zx^+xy^-3y2zz^ (i)…

Q4/ Find the flux of (D= zx + xy - 3y'z z^) out of a closed surface consisting of (1) the cylinder x' +y 4 between z= 0 and z =2; (2) the circular area with radius(r = 2) which bounds the cylinder at z = 0; (3) the corresponding circular area at z = 2. The surface is shown in the accompanying figure.

Q4/ Find the flux of (D= zx + xy - 3y'z z^) out of a closed surface consisting of (1) the cylinder x' +y 4 between z= 0 and z =2; (2) the circular area with radius(r = 2) which bounds the cylinder at z = 0; (3) the corresponding circular area at z = 2. The surface is shown in the accompanying figure.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Q4/ Find the flux of (D= zx + xy - 3y'z z") out of a closed surface consisting
of
(1) the cylinder x' +y? =4 between z= 0 and z =2;
(2) the circular area with radius(r = 2) which bounds the cylinder at z = 0;
(3) the corresponding circular area at z = 2. The surface is shown in the
accompanying figure.
Q5/Given A = e*x* +2cosyy + 2sinz", find V. A at the origin.
Q6/ Show that the divergence of E is zero if E= (100/r)0+ 40z.
Q7/ The region R < 2m (spherical coordinates) has a field E = (5R.10 /e0)R
(V/m). Find the net charge enclosed by the shell R= 2m.
Q8/ Given that D = (5R/4)R in spherical coordinates, evaluate both sides of
%3D
%3D
the divergence theorem for the volume enclosed between R = 1 and R = 2.
Q9/ Given that D = 10sinor*+ 2cos00" , evaluate both sides of the divergence
theorem for the volume enclosed by the shell r = 2.
Q10/ Given that D = (10r'/4)r in cylindrical coordinates, evaluate both sides
of the divergence theorem for the volume enclosed by r = 2, z = 0, and z = 10.
Q11/In a certain region, the electric field is given by
D = 2r(z + I)cosOr^ - r(z + 1)sin00° +r°cosOz^ µC/m?
(a) Find the charge density
(b) Calculate the total charge enclosed by the volume 0<r<2, 0<0< n/2,
0<z< 4.
(c) Confirm Gauss's law by finding the net flux through the surface of the
volume in (b).

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