Given a vector potential field configuration, A, (F) (xy)ỹ a) Calculate the magnetic field, B(F) b)...
task: (a) Check that it meets the vector potential condition , where B is a constant magnetic field. (b) Let A be the vector potential given under (a). Show that he is a member occurring in the Hamilotonian for a particle in the EM field equal to the expression for the interaction of the magnetic moment μL due to the orbital angular momentum with the magnetic field B where q is the charge and a m is the mass of...
part (a): express the magnetic field vector B created at the center O in terms of the current I, the radius vector R, and the length element vector ds part (b): What the direction of the magnetic field at point O? right, left, out of screen, downward, upward, or into the screen? part (c): Express the magnitude of the magnetic field at point O in terms of I and R. part (d): Calculate the numerical value of B, in tesla...
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.
2) What is the magnetic field B if the magnetic vector potential A is given by: Ā= 5e-29 + 3e 32. (25 pts.)
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A-(7, 0, 6) , B-(7, 3, 0) , C-(0, 3, 0) , D- (0,0,6), F-(7,0,0) Flux(B) (10 points) Un uniforme magnetic field B has constante strength...
please answer asap Sketch the vector field at the given points marked in the xy-plane. (a) =< 0, y > (b) F =<-x,y > Sketch the vector field at the given points marked in the xy-plane. (a) = (b) F =
Suppose you do a calculation for the magnetic field for some situation and you find B=PR 23 for some positive constants B. and R. a) sketch this field in the yz plane, Can this field be physical ? ,/ b) If this field is physical, find the current density J associated with this magnetic field. If the magnetic field is unphysical, devise a magnetic field that is physical by adding in a term and glve an example of a functional...
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B) (1 point) A uniform magnetic field B has constant strength b...
c. Let F : R³ → R³ be a vector field on R, given by the following function F(x, y, 2) = (x2)i + (y2)J + (xy)k. Calculate the flux of the field across the surface of the hemisphere, : [0, 1] × [0, 2x] → R³, where parametrized by the following function Þ(r, 0) = (r cos 0)i + (r sin 0) + (1 – 1²)!/2 k.
Please make it simple and clear to understand 3. A vector field is given by (a) Show that the vector field r is conservative. Then find a scalar potential function f(r,y,) such that r - gradf and f(0,0,0) 0 (b) By the result of (a) the following line integral is path independent. Using the scalar potential obtained in (a) evaluate the integral from (0,0,2) (where-y-0) to (4,2,3) (where -1,y 0,2) 4.2,3) J(0,0,2) 3. A vector field is given by (a)...