O Determine the y-coordinate of the centroid of the
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Q: Calculate the flux of the vector field F(x, y, z) (5x + 8)i through a disk of radius 7 centered at…
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Q: The figure above shows a contour consisting of two semicircular parts, of radii a and b respectively…
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- = Let er be the unit radial vector field. Compute the outward flux of the vector field F er/r² through the ellipsoid 4x² + 6y² + 9z² = 36. [Hint: Because F is not defined at zero, you cannot use the divergence theorem on the bounded region inside of S. ]Calculate the flux of vector field F = (xy°, x²y) across the circle of radius 1 centered at coordinates (0, –1).Assume a uniformly charged ring of radius R and charge Q produces an electric field E at a point Pon its axis, at distance x away from the center of the ring as in Figure a. Now the same charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius as in Figure a. How does the field Eick produced by the disk at P compare with the field produced by the ring at the same point? O O Ek Ering O impossible to determine
- Suppose a unidirectional vector field E exists across an enclosed surface A as shown below. which among the following is/are true? 153 E The divergence volume integral value will only be equal to 0 if E is a uniform field. O The divergence volume integral value will be positive if the magnitude of E is increasing along the positive z-hat direction. The divergence volume integral value will always be equal to 0. Only the top and bottom cylindrical phases have non-zero divergence surface integral values.consider the parallelepiped with sides: A=3i+2j+k، B=i+j+2k, c=i+3j+3k, then 1-Find the rolume of the paralldepiped 2-Find the area of the face determined by A and B. 3-Find the angle between the vactor C and the plane containing the face determined by A and BGive an example to show that a factor ring of an integral domain may be a field.