A)ifwe define the S transform as follows: E → M S: M → -E S. (For example Pe → Pm) or Then prove that Maxwell's general equations are invariant for this conversion. B) Show that the continuity equation holds for electric charges, and that magnetic charges also apply to their own continuity equation.
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- 5. The magnetic field is found to be B = (3(m f)f-m) for almost all space where m is an 4π 13 orienting, generating, a. b. C. time-and-space-independent vector. What are the units of m and what is it? What current distribution might generate B and prove it? What vector potential, A(7), might also generate B and prove it?A plane wave is propagating at a frequency of 100 MHz in a lossy medium. The amplitude of the electric field E at z=0 is equal to 200V/m. The medium is characterized by u=1 and &=2. 1. Find the propagation constant y after 1m: the amplitude of E loses 60% of its value and the its phase angle changes of 180'. 2. Find the conductivity a 3. Find the real and complex notations of the electric field 4. Find the expression of the magnetic field H 5. Deduce D and B 6. Find the expression of the Poyting vector 7. Find its average with respect to t.A proton, that is accelerated from rest through a potential of 14.0 kV enters the velocity filter, consisting of a parallel-plate capacitor and a magnetic field, shown below. 112 The E-field between the parallel capacitor plates is 1.1.105 N/C. What B-field is required so that the protons are not deflected? (Ignore relativistic effects for high velocities.) Submit Answer Tries 0/12 Send Feedback
- Faraday's Law Consider a square metal picture frame of side length s, mass M, and total electrical resistance R. It is dropped from rest from a height H above a region of uniform magnetic field pointing into the page. The frame accelerates downward under the influence of gravity until reaching the magnetic field. It is observed that, while entering the magnetic field, the frame moves with constant velocity. a. What is the frame's speed when it begins to enter the magnetic field? b. What is the strength of the magnetic field? Solve for B in terms of the given physical quantities (s, M, R and H), and any constants you need. c. After the frame has completely entered the magnetic field, what is the frame's acceleration? Justify your answer in two sentences or less. frame H X X XXXX X X X X X X X X X floora) The second of Maxwell's equations states that the divergence of the magnetic flux density is always zero, i.e. V B 0. What does this tell you generally about the distribution of magnetic flux? Describe the impact of a non-zero value on the right-hand-side of Maxwell's second equation. b) With reference to Figure 2, the Biot-Savart law can be used to show that the magnetic flux density due to a straight current-carrying wire of finite length is given by Hol %3D (cos a2 - cos a,) âg 477 Figure 2 Show that this expression is consistent with Ampère's law when applied to a long straight current carrying conductor. c) Figure 3 depicts a section of printed circuit carrying a current / of (100 + 10X) mA. The incoming and outgoing conductors are long, have negligible width and are connected at their ends by a conductive bridge where dA parallel‑plate capacitor has closely spaced plates. Charge is flowing onto the positive plate and off of the negative plate at the rate of i=delta q/ delta t =2.5 A. What is the displacement current i(d) through the capacitor between the plates? i(d) = ?A