6. A vector field is given as G=2x²ya, -2(2-x)a, + 3xyza. Prepare sketches of G₂, G₁, G₂, and IG, all evaluated along the line x = 2, y = -1, for 0 ≤ ≤ 10.
Q: (2-10) A charge q1 located at (4.5,3) m. -5 µC is located at (x,y)=(0,3) m. Another charge of q2 =…
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- 3. The electric field near a charged, large, thin, flat sheet of (let's say plastic) was obtained in Exercise 01 by solving a source charge integration problem. The electric field above a charged, flat disk of radius a was found to be: Ē = ok 2€ 1 √(a/z)² +1²° Then, we took the limit as the radius a tends toward infinity to obtain the much simpler expression E Ē = ok. 2€ 280 This same simpler equation can be very easily obtained by applying Gauss' Law using an appropriate Gaussian surface that extends above and below a small part of the charged sheet. Find this derivation (in a book or online) and rewrite it by hand below. Add verbal explanations to take the reader through the derivation, equation by equation.9) Pictured below is an ellipse oriented counterclockwise and a vector field F[X] plotted around it. B examining the figure determine if the flows along the oriented path and across it are positive or nega- tive in total. a) The flow around is positive and the flow out is positive. b) The flow around is negative and the flow out is positive. c) The flow around is negative and the flow out is negative. d) The flow around is positive and the flow out is negative. e) There is not enough information to determine the answer. -3 -2 -1 1 2 3) 213. In the following system: q1 = +8.0 µC, q2 = -6.00 µC, q3 = -10.0 µC. q2 6m q1 8m q3 a) Find the force on charge 3 due to charge 1, F13 . b) Find the force on charge 3 due to charge 2, F23 . c) Find the resultant force on charge 3, Fres . and its direction (angle Y)
- (2-10) A charge q1 = -5 µC is located at (x,y)=(0,3) m. Another charge of q2 = +4 µC is located at (4.5,3) m. O (0,0)2. A charge Q is uniformly distributed over a rod of length 1. Consider a hypothetical cube of edge I with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.16. Divergence of the function D çâr in spherical polar coordinates is %3D 4ar2 (a) Zero (b) 1 (c) 2 (d) 3 17. The dimension of µo€, is (a) L-2T² (b) L²T-2 (c) L-²T-2 (d) L²T²
- 3. A particular scalar field a is given by a. a=20 ex sin(πy/3) in Cartesian b. a=10psin() in cylindrical c. a=30cos(e)/r² in spherical find its Laplacian at P(-2,4,-6) for Cartesian, P(√2,π/2,7) for cylindrical and P(5, 30°, 60°) for spherical coordinate systems.2. Consider the radially symmetric flux field j = where = xi + yj + zk. (a) Show that the total flux through any closed surface that does not enclose the origin vanishes. (b) Show that the flux through any sphere centered at the origin is independent of the sphere radius.Problem 1 The figure below shows three concentric conducting thin spherical shells: • Sphere A of radius R₁ = 6 cm and a total charge QA = 2 nc. • Sphere-B of radius Rg = 21 cm and a total charge QB = -4 nC ⚫ Sphere-C of radius Rc 78 cm and a total charge Qc Qc is an unknown charge. Re RB RA B 1 What is the net electric flux o through the spherical surface of radius r = 13 cm from the center of the spheres? 2 spheres? E= 3. spheres? E= What is the magnitude of the electric field E at r = 59 cm from the center of the What is the magnitude of the electric field E at r=2 cm from the center of the 4. If the magnitude of the electric field is E 192 N/C at r = 93 cm from the center of the spheres, calculate Qc. Qe=
- 2.3. Two charges are the only charges in a particular region. Arranging a coordinate system so that = one (q1 0.10 C) is at the origin, the other (92 = 0.30 C) is located at the point (6.0 cm, 0). Find the magnitude and direction of the electric field at the following points: a) (3.0 cm, 0) b) (0, 3.0 cm) Be careful in part (b). It takes quite a bit of work, but once you see how to do it, you should see that the same routine can be used to calculate the field at every point in the coordinate system.#6. One the following vector fields F(x, y,z)= xyz*i+x²z*j+4x²yz°k G(x,y,z)= i+ (sin z) j+ y (cos z)k is conservative and other is not. (a) Determine whether F is conservative or not. (b) Determine whether G is conservative or not. (c) For the vector field that is conservative find a functionf such that the vector field is equal to Vf.5. Let F = -9zi+ (xe"² – 2xe²²)+ 12 k. Find ſg F .dø and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (see figure to the right), oriented upward. (a) Explain why the formula F à cannot be used to find the flux of F through the surface S. Please be specific and use a complete sentence.