total acceleration
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What is the total acceleration of a particle at (1,2) where the velocity field is
u = 3xy, v = -1.5y² + 5
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- Determine the phasor forms of the following instantaneous vector fields:(a) H = −10cos(106t + π/3)ax(b) E = 4cos(4y)cos(104t − 2x)az(c) D = 5sin(104t + π/3)ax − 8cos(104t − π/4)ayWhat is the net outward flux of the radial field F = ⟨x, y, z⟩across the sphere of radius 2 centered at the origin?A cylinder of radius a and height L is centered about the z -axis and has a uniform polarization alongits axis, P = P_0 z-hat. (P is a vector in the z direction).Find the electric field and electric displacement everywhere on its axis.
- Consider the special shape pictured in the diagram below. It is a cylinder, centered on the origin with its axis oriented along z, and it has been partially hollowed to leave two cone-shaped cavities at the top and bottom of the cylinder. The radius of the object is a, its height is 2a, and the solid part of the object (the shaded region that is visible in the rightmost panel of the illustration above, which shows a drawing of the cross-section of the object) has a uniform volume charge density of po. Assume that the object is spinning counter clockwise about its cylinder axis at an angular frequency of w. Which of the following operations is part of the calculation of the magnitude of the current density that is associated with the motion of the rotating object as a function of r (select all that apply)?y Figure 3: 7= xi+ yj+zk = pcos cos oi + p sin oj + zk = pp+ zk and i = dr dt -p sin oi + p cos oj + k = po + zk . Notice that cyclotron angular velocity we = do COS is a negative constant, i.e. in the figure the particle is circulating clockwise. 3. Consider a charged particle, q, in the presence of a magnetic field B with velocity i = it + üz = ü + ij at position relative to origin experiencing a magnetic force qü x B. From the second law it follows that the kinetic energy of the particle remains constant[ see figure 3] : d mv2 m[v² + v?] du - 0 = dt (a) : qü x B m ä - i [gữ x B] = ū. [m- = constant (True, False) dt 2 (b) : A [B x Č) Č [Ä x B] = B IC x A] (True, False)An ion enters a region of a uniform magnatic field Bout = 0.4T, with a speed v= 5*10^5 m/s. The ion makes a circular pathof radius r =9.4 mm. Then what is mass to charge ratio(m/q), (in ug/C) of the ion?