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Interface conditions for the polarization vector. Given the interface conditions for the electric field intensity and the electric flux density in Table 4.3:
(a) Find the interface conditions required for the polarization vector at the interface between two dielectrics of permittivity ε1 and ε2. First, assume no free charges on the interface and then allow for existence of free charges on the interface.
(b) Determine the ratio of the normal and tangential components of the polarization vector at the interface between two perfect dielectrics with permittivity ε1 and ε2 in terms of the relative permittivity of the two perfect dielectrics. Assume there are no charges at the interfaces.
For the vector field E = 5exp(-2r)rˆ - 3rzˆ calculate the divergence in cylindrical coordinates. Verify the divergence theorem for the cylindrical region enclosed by r=2, z=0 to 4.
Consider a permanent-magnet dc motor with the following parameters: Ra=0.35Ω, La=1.5 mH, Ke=0.5 V/(rads/s), Kt= 0.5 Nm/A, and Jm= 0.02 Kg.M^2. The rated torque of this motor is 4Nm.
Machine A was purchased three years ago for $10,000 and had an estimated market value of $1,700 at the end of its 10-year life. Annual operating costs are $1,350. The machine will perform satisfactorily for the next seven years.
Specify how many bits are needed to appropriately digitize each of the following signals. Choose from: 6 bits, 8 bits, 10 bits, 12 bits, 14 bits, or 16 bits. a. A signal where the maximum amplitude is 1 volt and the rms noise is 1.5 millivolts.
The power factor of a load connected to a 120-V 60-Hz source is raised from 0.866 lagging to 0.966 leading by connecting a 110.5-F capacitor in parallel with the load. Determine the load current I1 and the circuit current IT
A 50 ohm transmission line is terminated to the load (60-40j) ohm. How far from the load, a short ckt stub of a fix length of λ/8 needs to be placed so the minimum voltage standing wave ratio (VSWR) between generator and stub achieved. Find the VS..
A capacitor ofvalue 100[uF] is connected and charged through a voltage source of20V in series with a resistor of 10 ohms at t= 0s. What is thepower dissipated in the resistor at the beginning (t=0) and the power dissipated in the resistor after a ..
Problem (1): For the circuit shown in Figure PI: a) Using the Node-Voltage method. find the three nodes voltages VI. V2 and V3 b) Calculate the power delivered or absorbed by each source.
there is another issue associated with dams and fish and that is permitting enough flow to maintain downstream
Use Kirchhoff's current law to solve for the unknown currents.
the cross-section of a rectangular capacitor is shown below. it consists of a 12mm by 12mm conducting strip shielded by a 20 mm by 20mm rectangular conductor and separated by air. using the finite difference method,
A constant current I flows in the loop. Use the Biot-Savart Law to calculate the H -field along the z-axis.
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