Use Gauss's law to find the charge enclosed by the cube with vertices (±2, +2, +2) if the electric field is E(x, y, z) = xi + vj + zk.

Q: 4. Let D = y²z°ãx + 2xyz³ ày + 3xy?z² đz pC/m² in free space. a. Find the total electric flux…

A: Solution:-

Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

A:

Q: function u (t) == C, cos(@ot – ao) that would result if the mass on the spring were set in motion…

A:

Q: Verify that u is a solution to the equation ugx + Uyy + u zz = 0. u(x, y, z) = e4z+3y cos(5z)

A: Follow the procedure given below.

Q: ди ди ду ду Find the cauchy-riemann equations of, f (z) = | z | sin z. əx' dy'dx' ðy,

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. In…

Q: Question 3. Compute the integral dz 8+z where y is the rectangle with vertices +3+i with the…

A:

Q: Solve the Laplace equation in a cylinder vu = 0, 0<r < a, 0<:<1 u (r,0) = f (r) u (r, 1) = g (r) u…

A: Given: ∇2r=0 …1, 0&lt;r&lt;a, 0&lt;z&lt;1ur,0=frur,1=grua,z=0 We have to solve Laplace equation of a…

Q: If F= represents the flow of a liquid through a parabolic cylinder S: y=x, 0sxs2, 0szsl. That is…

A: If F→=y2,-x2,z2 represents the flow of a liquid through a parabolic cylinder S:y=x2,0≤x≤2,0≤z≤1.…

Q: السؤال 6 The electro static force given by (ke^2)/r^2, where k=1/ (4nE) 0 صواب İhi

A: False

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: 1. If F= (y,z,x), the outward flux through a smooth closed surface (a) depends on the surface. (b)…

A: Given, F=y,z,x We know,  Flux by the Gauss divergence theorem. ∬F.ds=∬∫divF.dvF=yi+zj+xk If you…

Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: divE = 0 divĦ = 0 curlĒ = %3| c Ət 1 DỂ curlĦ Using Maxwell's equations, show (V· V)Ē : c2 Ət?

A: Given:  ∇E=0∇H=0∇×E=-1c∂H∂t∇×H=1c∂E∂t

Q: A=LDU where D-) then the humber of special solubion s bo Ax =0 is equal a-1/b.e/c.2/d.camt be deubie…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Use Gauss' Law to find the charge enclosed by the cube with vertices (±1,±1±1) if the electric field…

A: Given The given electric field is Ex,y,z=x,y,z and the charge enclosed by the cube with vertices ±1,…

Q: Given F = (2xze*²z – 4, cos z, x²e*z – 3ycos?z sin z) 1. You are to show that the line integral S.…

A:

Q: Use Gauss's Law to find the charge contained in the solid hemisphere x2 + y2 + z² < a², z z 0, if…

A: Given:The Electric field, E→=xi⇀+yj⇀+7zk⇀Equation of solid hemisphere isx2+y2+z2≤a2       ,z≥0To…

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A:

Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: Show that the displacement u(x, t) in an elastic string of length t fireed at both ends which is set…

A:

Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…

A:

Q: A uniform electric field points in the :-direction, E = Ek. By explicitly calculating the surface…

A:

Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

A:

Q: Given the force field F = (2xze*z – 4, cos³z, x²e**z – 3ycos²z sin z) Solve for the work done by F…

A:

Q: (a) Suppose that a black hole has magnetic field F = (2a* + e" sin(2), y³ + xe*, 2z³ + e" cos(z) +…

A: TO FIND: Magnetic flux across the black hole

Q: Use Gauss's law to find the charge enclosed by the cube with vertices (±1,±1,±1) if the electric…

A:

Q: Find Laplace treins form for Ý +4Y+3Y = e y(o) =y co) = 1 %3D %3D

A: Formula Used:L{y''}=s2Y(s)-sy(0)-y'(0)L{y'}=sY(s)-y(0)L{eat}=1s-aL{tneat}=n!(s-a)n+1

Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

A:

Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

A:

Q: Evaluate the triple integral [ 2³ dV, where E is the solid tetrahedron with vertices (0,0,0),…

A:

Q: Use Gauss's law to find the charge enclosed by the cube with vertices (±2, ±2, ±2) if the electric…

A: The net charge enclosed by a closed surface S is given by Q=ε0∫∫s E.dS We can divide S into 6…

Q: Identify the work done, J. F.dr by an electric field, E = (x + xy)î + (y + 5)f – 5zk V/m to move an…

A: Work done along the curve C by vector field F . Where C is given by parametric equation r(t)…

Q: Let 0 < c < 1. Compute the integral rc+ioo dz Jc-ioo sin nz' where the integration path is the…

A: We will use the basic knowledge of complex line integrals to answer this question properly, in…

Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

A:

Q: For a certain fluid flow field the velocity is given by V = [y² – x(1+ x)]i+ [y(2x + 1)]j+k. Show…

A:

Q: Find the work done in moving a point charge Q- - 20 1C from.the origin to (4,0,0) m in the ficld E-+…

A: To find - Find the work done in moving a point charge Q = -20 μC from the origin to 4, 0, 0m in the…

Q: Evaluate /|/ (x² + y² + z²)² dV where E is the solid ball centered at the origin with radius 2.

A:

Q: Solve the sifferential equation using tHce Laplace transforms- you y =I y lo)=y'(0) = y"(0)= 6 %3D

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: eiz dz around (a) |z – in| = 2 (b)|z - | = 2 (c)|z| = 2 sinhz

A:

Q: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x=0, y=0.…

A: To draw graphs in 3d we need to find intersections with co ordinate axes and also with co ordinate…

Q: Calculate the work done by F(x,y) = ⟨2x + ln( 2y2 −1), arctan(y4 +2y +1) + 4xy / (2y2 − 1⟩ along the…

A:

Q: For an infinitely long conducting cylinder of radius a, with its axis coincident with its z-axis,…

A: The voltage is u(r,θ) It satisfies the Laplace equation, ∇2u=0 --&gt;equation(1) Equation(1)…

Q: find the flux of 3 – e")i+ (y³ + sin z)j+ (z³ – unded above by z = V4 – x² outward orientation.

A: We have to find the flux using the divergence therom according to the given information

Q: 2. Find the complex potential function f(z) = u + iv, given that 2u +3v = e*[cos(y) - sin (y)]. Also…

A:

Q: 3 2 Use a line integral to calculate the length of the helix ř(t) = (a cost, a sint, bt) 0<t < 2n…

A:

Q: The electric potential at each point (x,y) in the region R: x 2 0, y s1 is given by v - 48xy – 32x -…

A:

Q: Given the force field F = (2xze* - 4, cos°z, x?e**: - 3ycos?z sin z) Solve for the work done by F in…

A: