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Flux & Flux Density

Flux

Consider the space region bounded below by the right angled cone z=sqrt(x^2+y^2), and above by the sphere x^2+y^2+z^2=2. These two surfaces intersect in a horizontal circle, let T be the horizontal disk having this circle as boundary, S the spherical cap forming the upper surface, and U the cone forming the lower surface.

Surface integrals and flux

Find : Double of F*dS,over S, where F=(x*i+y*j+z*k)/(x^2+y^2+z^2) and where S is the surface of the infinite cylinder x^2+y^2=1; n pointing outward

Green's Theorem : Flux

Let C be a differentiable curve contained in the portion 0 inferior or equal to x inferior or equal to 1 of the first quadrant, starting on the positive y-axis and ending somewhere on the line x=1. Show that the flux of the vector field F F=(2xy-2x^4*y)i+(4x+4x^3y^2-y^2)j across C is always equal to -2. Hint : App

Flux : Circles

A) Let C be the unit circle, oriented counterclockwise, and consider the vector field F=i+j. Which portions of C contribute positively to the flux of F? Which portions contribute negatively? b) Same questions with F=x^2*y*i+x*y^2*j

Electrical Energy Conversion: Voltages & Currents

Question: Find the current I_N, required to establish a flux of 2 mWb in the air gap of the magnetic structure shown in the figure in the attached file. The structure is made of silicon sheet steel, and its magnetization curve is also shown. Assume that the coil has 500 turns, and the structure has the dimensions given in the at

Flux Across a Triangular Surface

SHOW ALL STEPS. Find the flux of F = xi + yj + zk across the surface S consisting of the triangular region of the plane 2x -2y + z = 2 that is cut out by the coordinate planes. Use an upward-pointing normal to orient S.

Electricity

Dry air will break down and generate a spark if the electric field exceeds about 2.95 x 10^6 N/C. How much charge could be packed onto a green pea (diameter 0.830cm) before the pea spontaneously discharges?

Calculating the Potential Difference

Question: Consider a generator constructed as shown in the attachment. The loop in this generator rotates at an angular rate of w. The slip rings in this design ensure that the same leg of the rotating loop is always connected to the same output terminal. Show that the potential difference between the output terminals is given b

Vector analysis

(a) Let F(x,y,z)=(x^2+y-4)i + (3xy)j + (2xy+z^2)k. Evaluate the double integral over S of (curl(F). dS) where S is the surface x^2 + y^2 + z^2 = 16, z >=0 (I) Using Stroke's theorem (II)By direct evaluation (b) Find the flux of the vector field F(x,y,z) = (y-x)i + (x+y)j + y k across the side of the triangle with vert

Coaxial cable: magnitude of the electric field; capacitance of the cable

Neglect end effects. The region between the conductors is air. Ke =1/4*pi*epsilon= 8.98755e9 N m^2/C^2. A coaxial cable has a charged inner conductor (with charge +4.8 microcoulombs and radius 1.199 mm) and a surrounding oppositely charged conductor (with charge -4.8 microcoulombs and radius 7.405 mm). a) What is the magn

Refrigeration Cycles and Heat Transfer

The air conditioner in a car uses R-134a, and the compressor power input is 1.5 kW, bringing the R-134a from 201.7 kPa to 1200 Kpa by compression. The cold space is a heat exchanger that cools 30 degrees C atmospheric air from the outside down to 10 degrees C and blows it into the car. What is the mass flow rate of the R-134a an

Compute the flux density in an iron core.

A magnetic circuit consists of an iron core of a cross sectional area of 4cm^2 in which an air gap is cut in, where a flux density of 0.9T is required. There is a leakage factor of 1.2 and fringing increases the cross sectional area of the gap by 10%. What should be the flux density in the iron?