3 - Given a scalar field T = (x+3)y² sin(2z) and a vector field A= r*yi+ y?(z+5)k, calculate (3) %3D %3D the following (1) Gradient of T: VT (2) Divergence of Ã: ỹ · Ã (3) Curl of Ã: ỹ × Ã
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- Determine the total charge(a) On line 0 < x < 5 m if ρL = 12 x2 mC/m(b) On the cylinder ρ = 3, 0 < z <4 m if ρs = ρz2 nC/m2(c) Within the sphere r = 4 m if ?? = 10 / (r sin ?) C/m3A closed surface with dimensions a = b = 0.400 m and c = 0.800 m is located as shown in the figure below. The left edge of the closed surface is located at position x = a. The electric field throughout the region is non-uniform and given by E = [ (yz2)i + (xz2+2)j +(2xyz-1)k] N/C, where x,y are in meters. Find the magnitude and direction of Efield at the point (0.5m,0.6m) Calculate the flux through each surface. What net charge is enclosed by the surfaceSolve for the net flux through each closed surface. -20 x 10c 3.0 x 10c (a) -3.0 x 106C 4.0 x 10c 5.0 x 106C (b) -2.0 x 10C (c) End cap of area 4.0 X 104 m a= 2.0 X 10 Cim? (d) Conductor + + + + + + +
- Q1) given the spherical surfaces of (r=l m and r-5 m), curry charge densities of (-20 nC/m and 30 nC/m) respectively, find (i) D at r=2.5 m (ii) The total flux leaving the outer surface (r-5).6) The hollow R radius cylindrical tube is infinitely long along the z-axis. The positive charges are evenly distributed over the surface of the tube, and the surface charge density σ. Find electric fields in both regions accordingly. A) r<R for D=0; r>R for D=arσR/r B) None. C) r<R for D=0; r>R for D=arσR/((\pi\)r) D) r<R for D=0; r>R for D=arπσR/r E) r<R for D=0; r>R for D=0 this is an electromagnetic wave lesson question.A flat surface of area 3.40 m? is rotated in a uniform electric field of magnitude E = 5.80 x 105 N/C. (a) Determine the electric flux through this area when the electric field is perpendicular to the surface. | N •m²/c (b) Determine the electric flux through this area when the electric field is parallel to the surface. N- m?/c
- There is a vertical electric field, 2.00 × 104N / C in magnitude, on the surface of the Earth on a day with an electrical storm. A car, with a rectangular dimension of 6.00 m by 3.00 m, travels along a dry gravel road that slopes downward at 10.0 °. Determine the electric flux in the chassis of the car.The electric field E, at one face of a parallelopiped is uni- form over the entire face and is directed out of the face. At the opposite face, the electric field E2 is also uniform over the entire face and is directed into that face (as shown in Fig. ). The two faces in question are inclined at 30° from the horizontal, while E, and E₂ (both horizon- tal) have magnitudes of 2.50 x 104 N/C and 7.00 × 104 N/C. Assuming that no other electric field lines cross the surfaces of the parallelopiped, determine the net charge contained within. a. -67.5 80 C c. 105 o C : 005 E₁ *74 کار کیا Fig. 6.00 cm LL b. 37.5 80 C d. - 105 & C E₂ 30°