If two magnetic field vectors H, and H2 are moving along the same axis in free space, write all the possible base vectors.
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- A particle of mass m, charge q and position x moves in a constant, uniform magnetic field B which points in a horizontal direction. The particle is also under the influence of gravity, g , acting vertically downwards. Write down the equation of motion and show that it is invariant under translations x -> x + x0. Obtain x = \alpha x \times n + gt + a where \alpha = qB/m, n is a unit vector in the direction of B and a is a constant vector. Show that, with a suitable choice of origin, a can be written in the form a = an. By choosing suitable axes, show that the particle undergoes a helical motion with a constant horizontal drift. Suppose that you now wish to eliminate the drift by imposing a uniform electric field E. Determine the direction and magnitude of E. TrainingQuestion A5 Consider an infinitely large sheet lying in the zz-plane at the origin, the extent of the sheet in the x, and z direction is infinite. The sheet carries surface current J = Jok, where Jo is the current per unit width perpendicular to the flow. Calculate the magnetic field everywhere (y > 0 and y < 0) due to J. Sketch the Amperian loop.A particle of charge q moves in a circle of radius a at constant angular velocity w. (Assume that the circle lies in the xy plane, centered at the origin, and at time t=0 the charge is at (a,0), on the positive x axis.) a) Find the electric and magnetic fields at the center. b) From your formula for B you obtained in a), determine the magnetic field at the center of a circular loop carrying a steady current I.
- An electron of mass m and charge -e is moving through a uniform magnetic field B (Figure 1)At the origin, it has velocity v = (vz, Vy, 0), where vz > 0 and vy > 0. A screen is mounted = (B1, 0, 0) in vacuum. Part A perpendicular to the x axis at a distance D from the origin. First, suppose B= 0. Find the y coordinate y of the point at which the electron strikes the screen. Express your answer in terms of D and the velocity components vz and vy. Throughout, you can assume that the effect of gravity is negligible. • View Available Hint(s) Figure 1 of 1 y = y B Part B Now suppose Bx > 0, and another electron is projected in the same manner. Which of the following is the most accurate qualitative description of the electron's motion once it enters the region of nonzero magnetic field? screen The electron decelerates before coming to a halt and turning around while always moving along a straight lineA long straight cylindrical shell has an inner radius R; and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r < R;). The magnetic field is zero everywhere in the hollow region. We conclude that the wire: O is on the cylinder axis and carries current i in the same direction as the current in the shell may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell O does not carry any currentConsider two infinitely long and parallel wires separated by distance d and carrying currents I₁ = -12. (a) Find the magnitude and direction of the vector potential A(r1,72) at a point P where r₁ and r2 represent the distances to P from wire 1 and wire 2 respectively. (b) What is the magnitude of A for r₁ = r₂? (c) What is the value of the magnetic field B for r₁ = r₂? (d) Given that B = V x A, how can you reconcile the answers to (b) and (c) above?
- b) A conductor lies in a magnetic field. The current flowing through the conductor is I = (5,9,4). The magnetic flux density is B = (–2, 4, 6). Calculate the electromagnetic force acting on the conductor by F = I x B.A particle of charge Q is located outside an infinitely long cylinder whose axis points out of the page on which is wrapped an infinitely long current-carrying wire with steady current I. If the particle is launched with speed Vo, determine the directions such that it experiences zero magnetic force. left or right in or out up or down the force is maximum any directionThree long, straight wires are seen end-on in the figure below. The distance between the wires is r= 0.254 m. Wires A and B carry current IA = IB = 1.51 A, and wire C carries current Ic = 3.30 A. Assume (for example) the only forces exerted on wire A are due to wires B and C. Find the force per unit length exerted on the following. (Express your answers vector form.) B (a) wire A (b) wire B IB TA N/m N/m Ic X