515P) Calculate (r is the usual position vector: (coser), (ri), 7 x(x B) where B is...
Calculate (r is the usual position vector: (cose/r?), 7(rr), Yx(FxB) where B is constant vector along z direction.
515P) Calculate (r is the usual position vector): 7:7, 7(r-), r •7(r) integrate this over a spherical volume radius b centered at origin: convert this to surface and volume integral.
(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...
2. Consider a static volume current density J(r') where r' is the position vector of a point in the current distribution. Show that the field generated at a point with position vector r, according to the Biot-Savart law, u mrJ(r')RJ B(r) = -JJJp3 av, 477 o in which R=r-r' and R=R , satisfies Maxwell's magnetostatic equation V x B = 4J (u should be considered as constant). Consider the magnetic vector potential defined by A and the Lorenz gauge Show...
Consider the vector field (-7.-2.3) xr, where r= = (x,y,z). a. Compute the curl of the field and verify that it has the same direction as the axis of rotation b. Compute the magnitude of the curl of the field. a. The curl of the field is (i+O; Ok b. The magnitude of the curl of the field is (Type an exact answer, using radicals as needed.)
(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...
5. If ||2|| := VxTx is the usual (Euclidean) length of a vector x E R”, show that the vector Qx has the same length whenever Q is an orthogonal n xn matrix. If we define the angle between vectors x, y E R” as Z(x,y) := cos-1 -1 / xTy \ ||3||||y|| show that the angle between Qx and Qy is unchanged.
The general process (not referenced to Figure 1) to calculate the moment of a force about a specified axis is as follows:The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q ) can be calculated using the scalar triple product,MPQ=uPQ · r × Fwhere r is a position vector from any point on the line through P...
Problem 3. Let D be the vector space of all differentiable function R wth the usual pointwise addition and scalar multiplication of functions. In other words, for f, g E D and λ E R the function R defined by: (f +Ag) ()-f(r) +Ag(x) Let R be four functions defined by: s(x)-: sin 11 c(r) : cosz, co(z)--cos(z + θ), and so(r) sin(z + θ), and Wspanls, c Which of the following statements are true: (a) For each fixed θ...
The position vector of a particle points along the positive direction of a Z axis. If the torque of the particle is (a) Zero (b) in the negative direction of x, and (c) in the negative direction of Y, in what direction is the force causing the torque?