Có 60+ tài liệu thuộc chủ đề "giáo trình giảng dạy"
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With B proportional to H or for uniform magnetization, the divergence of H is also zero so that the scalar magnetic potential obeys Laplace's equation in each region:. 366 The Magnetic Field. The associated magnetic field is then H=VX =Ii. R (9) For the three cases, the magnetic field far from the sphere must approach the uniform applied field:. The...
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A charge q of mass m moves through a uniform magnetic field Boi,. (a) What is the subsequent velocity and displacement?. What is the radius of this circle and where is its center?. (c) What is the time dependence of the kinetic energy of the charge 2mlvl 2?. A trans- verse magnetic field Boi, is applied. (a) What is the...
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(d) If we assume that there is one such dipole within each volume of a 3 , what is the permeability of the medium?. An orbiting electron with magnetic moment mi, is in a uniform magnetic field Boi, when at t = 0 it is slightly dis- placed so that its angular momentum L. (a) Show that the torque equation...
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When the switch was later opened, another transient current flowed in loop 2, this time in the same direction as the original current in loop 1. Currents are induced in loop 2 whenever a time varying magnetic flux due to loop 1 passes through it.. In general, a time varying magnetic flux can pass through a circuit due to its...
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The simple magnetic circuit in Figure 6-8 has an N turn coil wrapped around a core with very high relative permeability idealized to be infinite. There is a small air gap of length s in the core. In the core, the magnetic flux density B is proportional to the magnetic field intensity H by an infinite permeability g. The B...
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For a noninfinite core permeability, k is less than unity because some of the flux of each coil goes into the free space region and does not link the other coil. In an ideal transformer, where the permeabil- ity is infinite, there is no leakage flux so that k = 1.. Because with no leakage, the mutual inductance is related...
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Such a model may help explain the periodic reversals in the earth's magnetic field every few hundred thousand years.. If the field winding of a motor is excited by a dc current, as in Figure 6-18, with the rotor terminals connected to a generator whose field and rotor terminals are in series, the circuit equation is. The angular speed of...
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If the flux (D itself depends on the number of turns, as in Figure 6-24b, there may be a contribution to the voltage even if the exciting current is dc. This is true for the turns being wound onto the cylinder in Figure 6-24b. For the tap changing configuration in Figure 6-24c, with uniformly wound turns, the ratio of turns...
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Figure 6-28 (a) A conducting material moving through a magnetic field tends to pull the magnetic field and current density with it. (b) The magnetic field and current density are greatly disturbed by the flow when the magnetic Reynolds number is large, R. Since (41) is linear, the most general solution is just the sum of the two allowed solutions,....
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Remember that in (16) and (17) the currents and vector potentials are all evaluated at their final values as opposed to (11), where the current must be expressed as a function of flux.. This stored energy can be thought of as being stored in the magnetic field. AdV= (VxH)"AdV (18) where the volume V is just the volume occupied by...
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High permeability material is attracted to regions of stronger magnetic field. (a) Find the mutual inductance M and resistance R of the loop. and has a self-inductance L.. What is the time dependence of the induced short circuit current when the line current is instantaneously stepped on to a dc level I at t = 0?. (d) If the loop...
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(a) What is the open circuit Hall voltage? (Hint:. transverse current of each carrier must be zero.) (b) What is the short circuit Hall current?. (a) What is the magnetic flux density everywhere? Find the electromotive force (EMF) of the loop for each of the follow- ing cases.. (b) A highly conducting circuit abcd is moving downward with constant velocity...
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Until Faraday showed that a time varying magnetic field generates an electric field, it was thought that the electric and magnetic fields were distinct and uncoupled.. Circuit theory assumes that the electric and magnetic fields are highly localized within the circuit elements. V.J = 0=>JdS = E ik= (8) Similarly, time varying magnetic flux that is dominant within inductors and...
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A simple rule for the time average of products is obtained by realizing that the real part of a complex number is equal to one half the sum of the complex number and its conjugate (denoted by a superscript asterisk). as the complex exponential terms e 2iW". average to zero over a period T = 2ir/w and we again realized...
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Sinusoidal Time Variations 505. If the velocity v is much less than the speed of light, (34) reduces to the Galilean transformations,. The coordinates perpendicular to the motion are unaffected by the relative velocity between reference frames. Continued development of the theory of relativity is be- yond the scope of this text and is worth a course unto itself.. 7-4...
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while the second has its electric field polarized in the y direc- tion. Each solution alone is said to be linearly polarized because the electric field always points in the same direction for all time. If both field solutions are present, the direction of net electric field varies with time. In particular, let us say that the x and y...
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We can easily explore the effect of losses in the low and large loss limits.. If the Ohmic conductivity is small, we can neglect it in all terms except in the wavenumber k 2. For large conductivities so that the displacement current is negligible in medium 2, the wavenumber and impedance in region 2 are complex:. The fields decay within...
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There are no transmitted fields within the perfect conductor, but there is a reflected field with power flow at angle 0, from the interface normal. kx,= k sin 0, k,,=k cos 0,(4). At this point we do not know the angle of reflection 0, or the reflected amplitude E,. They will be determined from the boundary conditions at z =...
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Therefore, a Brewster's angle of no reflection only exists if the H field is parallel to the boundary.. At the critical angle, which can only exist if light travels from a high index of refraction material (low light velocity) to one of low index (high light velocity), there is a transmitted field that decays with distance as a nonuniform plane...
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i t ] what are the spatial dependences of the fields?. Find the electric and magnetic fields if the sheet is placed within an Ohmic conductor or within a plasma.. (b) Find the electric and magnetic fields within and outside the current distribution.. (c) How much time-average power per unit area is delivered by the current?. (d) How does this...