A current filament carrying 15 A in the a, direction lies along the entire z axis. Find H (in A/m) in rectangular coordinates at P(4, 3,0).
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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. TrainingConsider an infinite hollow conducting cylinder of inner radius R and outer radius 3R, as shown. The non-uniform current density J is out of the page and varies with distance r fromthe center as J=J0rk (k is k hat) where J0 is a positive constant. Calculate the magnetic field at point P (r = 2R) from the centre,(magnitude and direction). Sketch the Amperian loop.function of r for each region below, in terms of a, b, and any physical page, uniformly distributed along its surface. Find the magnetic field as a through its cross-section, and the shell carries a total current /, into the thick wire carries a total current 1 out of the page, uniformly distributed thin cylindrical shell of radius b. (Neglect the thickness of the shell.) The A long, thick cylindrical wire of radius a is surrounded by a long. B6. 1. or numerical constants, and circle its direction. (a) B(a b) outside the shell Circle the direction: (clockwise ) (counter-clockwise ) (another direction) (there is no field)
- Biot-Savart’ s Law. 2. Line x = O, y = 0, 0 ¡ z ¡ 10 m carries current 2 A along az. Calculate H at points:(a) (5,5,0)(b) (5,15,0)(c) (5,-15,0)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.do P(0,0.2) R FIGURE 3-11 A uniformly charged disk (Example 3-8).
- A 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?