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A uniform magnetic field B has constant strength b teslas in the z-direction L.e, B- (0,0,b) (a) ...
A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B =...
A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0,0, b) ] (a) Verify that A = Bxr is a vector potential for B, where r = (x, y,0) (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A = (3,0,2), B = (3,3,0), C = (0,3,0), D= (0,0,2), F = (3,0,0) Flux(B) =
(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...
(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...
Next Problem List Previous (1 point) B = (0,0, b) 1 A uniform magnetic field B...
Next Problem List Previous (1 point) B = (0,0, b) 1 A uniform magnetic field B has constant strength b teslas in the z-direction [ie. (a, y, 0 Bxr is a vector potential for B, where r (a) Verity that A (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B. C, and D in Figure 17 C F FIGURE 17 A (8,0,7), B (8,5,0), C (0,5,0), D (0,0,7), F (8,0,0) Flux(B)...
(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 f...
(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...
Recall that it is conservative, then the line intera/ F.dr is path-independent meaning that the the...
Recall that it is conservative, then the line intera/ F.dr is path-independent meaning that the the integral depends only on the initial and terminal bolets of the sath, and not on the path Similar ideas are true for surfaces, although we must now discuss the curl instead of the gradient. Note that there is some vector field A such that (V x A) = F. then Suo ' Theorem tells us that JP as - x A). S = 6...
The behavior of a spin- particle in a uniform magnetic field in the z-direction, , with...
The behavior of a spin-
particle in a uniform magnetic field in the z-direction,
, with the Hamiltonian
You found that the expectation value of the spin vector
undergoes Larmor precession about the z axis. In this sense, we can
view it as an analogue to a rotating coin, choosing the
eigenstate with eigenvalue
to represent heads and the eigenstate with eigenvalue
to represent tails. Under time-evolution in the magnetic field,
these eigenstates will “rotate” between each other.
(a) Suppose...
A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure)
A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure). It what direction is the net force on the wire rectangle? A) out of page B) up C) down D) force is zero E) left 8) A solid cylinder of radius R = 5.0 mm caries a uniform current density of 1.50 x 106 A/m2. What is the magnitude of the magnetic...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly,...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
2. A steady, uniform magnetic field B with unknown magnitude and direction exists throughR out the shaded rectangula...
2. A steady, uniform magnetic field B with unknown magnitude and direction exists throughR out the shaded rectangular region shown here (diagrams are not to scale). This region is planar-entirely in the r-y plane (+x is east and +y is north). The region's width (from its west edge to its east edge) is a known distance D. The region's length (from its north edge to its south edge) is 10D. Consider the following experiments, all performed with this field. Experiment...
Iwire The magnetic field for a long wire is В — B = 2π r =...
Iwire The magnetic field for a long wire is В — B = 2π r = distance from wire, I = current d through wire, Ho = 4 n x 10~-7 Tm Iloop A Current-carrying wire in magnetic field B the magnetic force on the wire is I = current, L = vector, magnitude is length of the wire, direction of the curent The magnetic forces between wires is one way to measure currents without having to place an ammeter...
A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0,0, b) ] (a) Verify that A = Bxr is a vector potential for B, where r = (x, y,0) (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A = (3,0,2), B = (3,3,0), C = (0,3,0), D= (0,0,2), F = (3,0,0) Flux(B) =
(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...
Next Problem List Previous (1 point) B = (0,0, b) 1 A uniform magnetic field B has constant strength b teslas in the z-direction [ie. (a, y, 0 Bxr is a vector potential for B, where r (a) Verity that A (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B. C, and D in Figure 17 C F FIGURE 17 A (8,0,7), B (8,5,0), C (0,5,0), D (0,0,7), F (8,0,0) Flux(B)...
(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...
Recall that it is conservative, then the line intera/ F.dr is path-independent meaning that the the integral depends only on the initial and terminal bolets of the sath, and not on the path Similar ideas are true for surfaces, although we must now discuss the curl instead of the gradient. Note that there is some vector field A such that (V x A) = F. then Suo ' Theorem tells us that JP as - x A). S = 6...
The behavior of a spin-
particle in a uniform magnetic field in the z-direction,
, with the Hamiltonian
You found that the expectation value of the spin vector
undergoes Larmor precession about the z axis. In this sense, we can
view it as an analogue to a rotating coin, choosing the
eigenstate with eigenvalue
to represent heads and the eigenstate with eigenvalue
to represent tails. Under time-evolution in the magnetic field,
these eigenstates will “rotate” between each other.
(a) Suppose...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
2. A steady, uniform magnetic field B with unknown magnitude and direction exists throughR out the shaded rectangular region shown here (diagrams are not to scale). This region is planar-entirely in the r-y plane (+x is east and +y is north). The region's width (from its west edge to its east edge) is a known distance D. The region's length (from its north edge to its south edge) is 10D. Consider the following experiments, all performed with this field. Experiment...
Iwire The magnetic field for a long wire is В — B = 2π r = distance from wire, I = current d through wire, Ho = 4 n x 10~-7 Tm Iloop A Current-carrying wire in magnetic field B the magnetic force on the wire is I = current, L = vector, magnitude is length of the wire, direction of the curent The magnetic forces between wires is one way to measure currents without having to place an ammeter...
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