(1 point) Evaluate the circulation of yi zj+6yk around a square of side 7. centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis Circulatio...
8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin 8) Find the circulation of F =(6x+5 y,4y+3z, 2x+1z) around a square of side 7, centered at (1,2,1), lying in the plane 4x+1y+6z = 12 , and oriented clockwise when viewed from the origin
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F around a circle C of radius 0.1, centered at the origin, if C is on the ry- yz-, and rz-plane respectively oriented counter-clockwise when viewed from the positive z, positive a, and positive y-axis respectively 7. Three small squares Ci,C2, Cs each with sides 0.1, centered at the...
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
Use Stokes' Theorem to evaluate integral_C F middot dr. C is oriented counterclockwise as viewed from above. F(x, y, z) = yz i + 8xz j + e^xy k C is the circle x^2 + y^2 = 1, z = 2.
Use Stokes' Theorem to evaluate F. dr where Cis oriented counterclockwise as viewed from above. F(x, y, z) - xy + 27 + 6yk, C is the curve of intersection of the plane X + 2-1 and the cylinder + 9.
3. A charge O is uniformly distributed around a thin plastic ring lying in the yz-plane with the ring center at the origin O. A charge q is located on the x-axis a distance d from the origin. If the ring radius is R, develop an expression for the amount of work that must be done by an extemal force to move charge q to the point O. Assume that both O and q have the same sign: that is,...
1. A square conductive loop of side 10.0 cm is centered in the x-y plane. It carries a 10.0 mA current clockwise when viewed from the +z direction. Find H(0, 0, 16 cm).
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis. Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
6. (4 pts) Vectors VÀ and VB generate a square in the plane x +2y + 3z = 1, as shown in the left figure. A smooth vector field F in the square behaves as shown in the right figure. В ID 18 12 10 0 B 10 14 16 18 А Assume that the greatest circulation density of T at P is 5 and at Q is 2. (a) Find curl at P. (b) Find curlī at Q. (c)...
Problem 1 A -2.80 jIC point charge is fixed at the origin of the x axis A-7.80 pC point charge of mass 1.50 grams is moving along the x axis from the "x direction toward the charge at the origin. It has a speed of 22.0 m/s when it is at x -0.800 mIgnore gravity. Calculate (a) the total energy of the-7.80 pC when it is at r-0.800 m. 0.609 (b) the position along the x axis where the speed...