Consider the electrostatic field e=k[y^2i+ (2xy+z^2)j+ 2yzk] calculate the potential of this field using the origin as a reference
Consider the electrostatic field e=k[y^2i+ (2xy+z^2)j+ 2yzk] calculate the potential of this field using the origin...
The equation of electric potential in space is given by: V(x,y,z) = 2xy/x 1. Calculate the electric potential at point (x = 1, y = -2, z = 3) in space. 2. Find the electric field E vector as a function of x, y, z. 3. Calculate the electric field at point (x = 1, y = -2, z = 3) in space.
(a) Given the vector field F = (0,22 + 2xy) = ui + (x2 + 2xy)j Find u for 7 to be conservative and find the potential, if it exists (b) Given u= (e? – zły, xy + y) = (e– r’y)i + (xy + y); Evaluate I= dos u dr where is the circle with radius r = 1 and center at the origin.
Given the velocity field j = 101 +(x2 + y2)7 - 2xy K (m/s) a) b) c) Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of (x, y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m? d)
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
F(x, y,z)=(y2 +e", 2xy + z sin y, cos y) is a gradient vector field. Compute Sc F. dr where C=GUC,, C işthe curve y = x^, z = 0 from (0,0,0) to (1,1,0) and C, is the straight line from (1,1,0) to (2,2,3)
2. A) Calculate the work done by the field } = (x² - y2,-2xy) when moving an object from the origin to the point (1, 2) along the path C: x = t?, y = 2t. B) Use a Theorem from 16.3 to determine whether or not F = (x2 - y2,-2xy) is a conservative vector field. C) Deduce the work done by the field } = (x2 - y2,-2xy) moving an object from the point (1, 2) to the...
A cube sits in an electric field by E (2i+3j-2 k). One corner of a cube is at the origin with the opposite corner located at (1, 1. 1) m. What is the net (lux through the cube in c. 0 e. None of these
F(x,y,z)= (y² +e",2xy +z sin y, -cos y) is a gradient vector field. Compute Sc F. dr where C=C UC2, C, is the curve y=x*, z =0 from (0,0,0) to (1,1,0) and C, is the straight line from (1,1,0) to (2,2,3).
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.
b- Consider the vector field F(x,y,z)= (3x²y2-3ze, 2xy +2sin z, - 3x02 + 2ycos z). (a) if f(x,y,z) = axºy2+be*2 + cysin z then a =......, (b) Use the fundamental theorem of LINE INTEGRAL to evaluate Y = SF-di along the curve defined by the parametrization F(t)= (1, sint, t-T) for Osts. Y = ...... b Choose... Y = Choose.... Choose... Choose...