8. A vector field F is given in cylindrical polar coordinates by F(p₁6, 2) == cos(7²)₂ Find the outward flux of F across the curved surface of a cylinder of radius a and height h located with its centre at the origin and its axis on the z axis. Find also the outward flux of F across the plane end faces of the cylinder. What is the next outward flux of F across the whole cylinder?

Q: A yacht sets off from the port in Abu Dhabi and travels 350 km at 145' towards the Persian Gulf and…

A:

Q: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

A:

Q: X p(x, y, z)=xz²+sin (y) ex

A:

Q: A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1…

A: Stoke's theorem ∫CF→.dr→=∫∫S curlF→.dS→ Where S is a smooth surface bounded by a smooth closed curve…

Q: three decimal pI 1.1 ,Yi = i 2.51 X2 = i 1.2 ,Y2 = i 3.273 X3 = i 1.3 Y3 = 4.50283 X4 = i 1.4 Y4 =…

A: Consider the equation

Q: Ans. (5) Given position vector r(t) = (t₁ t - sint, 1- cast) ⇒ r (t) = ti + (t-sint) 3 + (1 - cost)…

A: Ans. (5) Given position vector

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

A:

Q: (a) A filament is formed into a circle of radius a, centered at the origin in the plane z = 0.…

A: For Biot-Savart law dH=μ04πIdl×rr3=μ0Idlsinθ4πr2 gives the magnetic field produces at a point due to…

Q: A parametric curve C is given by the position vector F(1)=sin(21). sin" (+),e' osis Osis". a) Find…

A: a)The given position vector is, r→(t)=12sin(2t),sin2t,et

Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then if…

A:

Q: 3. Let F = (x - y, xy) and C be arc of the circle x? + y? = 4 traversed counter-clockwise from (2,0)…

A:

Q: Find the curl of the vector field F curl F = (2y cos(x), 5x sin(y))

A: F = (2ycosx , 5xsiny) find curl F =?   curl F  = dF2/dx - dF1/dy here  F1 = 2ycosx  F2 = 5xsiny now…

Q: Sketch a directional field for the equation. Identify at least 3 isoclines. dy dx =y-x+2

A: This is a problem of slope field.

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: 1-2 Find the domain of the vector function. 1. r(t) = (10(1 In(t + 1), t - 2:21

A:

Q: 3. The position vector of a particle moving in the plane is given by r(t) = e *'i+ e'j. a) Find the…

A:

Q: Calculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to…

A:

Q: Given a velocity field: V = 1.8 ( rz (1-sin²(0))) er + 2.8 (1-cos2(0)+ rz) eg +1.8 ( rz tan(0)…

A:

Q: Identify the direction from graph of functions given below: vector i) r = i(2 cos 21)+ j(2sin 2r) ;…

A: Given, r→=i^(2cos2t)+j^(2sin2t) Identify the direction vector, From the given position vector,…

Q: On a metal plate in the shape of a rectangle, the temperature at a point (x,y) is given by; 100 3x²…

A:

Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

A:

Q: 6. What is the corresponding vector fieldV for the scalar potential p(x, y)= In(x+ ¥)?

A:

Q: Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: A particle travels along the curve r(t) = (cos t, sin t, In(cos t)). a) Find the distance the…

A:

Q: Find the work done by the force field F = in moving the particle from the point (3, 0, 0) to the…

A:

Q: 3. Find an equation of the plane tangent to the Bohemian dome S described by the vector function…

A:

Q: Use Newton's Second Law of Motion to find the force required so that a particle of mass 2 has…

A: Given: m=2r(t)=⟨t2,t4,sin(2t)⟩

Q: 1. State whether the following are scalar or vector quantities: (a) A temperature of 50 °C (b) A…

A: (a) Temperature possesses only magnitude, as in the given case 50 deg. Celsius but does not have…