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Calculate (r is the usual position vector: (cose/r?), 7(rr), Yx(FxB) where B is constant vector along...
515P) Calculate (r is the usual position vector: (coser), (ri), 7 x(x B) 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.
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?
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...
(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...
(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...
7. A point P moves along the spiral rae20 with constant speed u. Show that the components of its velocity along and perpendicular to the radius vector are constant. Find in terms of u and r the magnitude of the resultant acceleration of P. Find the angle between this acceleration and the velocity of P
7. A point P moves along the spiral rae20 with constant speed u. Show that the components of its velocity along and perpendicular to the...
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...
A particle moves so that its position vector is given by r -coswt i+sin wt j where w is constant a. Show that the velocityof the particle is perpendicular tor . b. Find the magnitude of acceleration in the direction of 2-h C. Show that dt