A parallel-plate capacitor with plate separation d is connected to a source of emf that places a time-dependent voltage V(t) across its circular plates of radius r0and area
(a) Write an expression for the time rate of change of energy inside the capacitor in terms of V(t) and dV(t)/ dt.
(b) Assuming that V(t) is increasing with time, identify the directions of the elecuic field lines inside the capacitor and of the magnetic field lines at the edge of the region between the plates, and then the direction of the Poynting vector
(c) Obtain expressions for the time dependence of E(t), for
B(t) from the displacement current, and for the magnitude of the Poynting vector at the edge of the region between the plates.
(d) From
(e) Compare the results of pails (a) and (d) and explain the relationship between them.
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
University Physics Volume 2
Additional Science Textbook Solutions
Essential University Physics: Volume 2 (3rd Edition)
Conceptual Physical Science (6th Edition)
College Physics
Introduction to Electrodynamics
Physics for Scientists and Engineers with Modern Physics
Life in the Universe (4th Edition)
- A series electric circuit contains a resistor R, a capacitor C and a battery supplying a time-varyingelectromotive force V(t). The charge q on the capacitor therefore obeys the equation R(dq/dt) + (q/C) = V(t) Assuming that initially there is no charge on the capacitor, and given that = sinωt V(t) V0 , findthe charge on the capacitor as a function of time. [Hint: First, find an appropriate integrating factor.]arrow_forwardCompute the capacitance of the capacitor in the defibrillator and calculate the magnitude of the averagecurrent flowing during the pulse.Hint: The relation between the stored charge (Q), and the voltage across the capacitor is given byIn a charged capacitor, positive charges are on one side of the plate, and negative charges are on the other.The amount of energy (E) stored in such a configuration is given byCurrents in the range of a few amperes flowing in the region of the heart can cause death within a few minutes. In thisconnection, a large current of about 10 A is often less dangerous than a 1-A current. When the smaller current passes through the heart,it may tetanize only part of the heart, thereby causing a desynchronization of the heart action; this condition is called fibrillation. Themovements of the heart become erratic and ineffective in pumping blood. Usually fibrillation does not stop when the current source isremoved. A large current tetanizes the whole heart, and when…arrow_forwardA large capacitor of 3000 µF is charged by a constant current. After 1 minute it reaches a voltage of 100 V. At that voltage, the charging circuit is disconnected. a) Calculate the charging current. b) A second identical capacitor is connected across the capacitor, using wires with 1 kN re- sistance. Sketch a graph of the voltages on the two capacitors as a function of time, with appropriate numbers and units marked on the axes.arrow_forward
- A simple series circuit consists of a 160 resistor, a 28.0 V battery, a switch, and a 3.20 pF parallel-plate capacitor (initially uncharged) with Os. plates 5.0 mm apart. The switch is closed at t = ▼ Part A After the switch is closed, find the maximum electric flux through the capacitor. VE ΑΣΦ Submit Part B 0.175 A Submit After the switch is closed, find the maximum displacement current through the capacitor. Part C Request Answer ✓ Correct Previous Answers Find the electric flux at t Submit ΨΕΙ ΑΣΦ Part D = 0.50 ns. Request Answer - ΑΣΦ Find the displacement current at t ? wwwww. 0.50 ns. 5 2. ? V. m ? V. marrow_forwardA 1·21-MF Capacitor is connected to a North American electrical outlet. (Avrms = 120V, f = 60·0Hz). Assuming energy stored in the Capacitor is Zero at + = 0, determine the magnitude & the current in the wires at t = 192 Note 3 Answer must be in A. S thearrow_forwardA parallel-plate vacuum capacitor is connected to a battery and charged until the stored electric energy is U. The battery is removed, and then a dielectric material with dielectric constant K is inserted into the capacitor, filling the space between the plates. Finally, the capacitor is fully discharged through a resistor (which is connected across the capacitor terminals). Find Ur, the the energy dissipated in the resistor. Consider the same situation as in the previous part, except that the charging battery remains connected while the dielectric is inserted.(Figure 2) The battery is then disconnected and the capacitor is discharged. For this situation, what is Ur, the energy dissipated in the resistor?arrow_forward
- A capacitor, C is connected across an emf given by: v(t) = Vo sin(wt) %3D Write an expression for the current through the capacitor. I(t) = %3Darrow_forwardThe image attached is a neat copy of a photo of an electricity meter for a domestic solar array. The display shows the energy we sold to the electricity company on a winter's day. Each box is 100 W high and 1 hr wide. At the radius of the earth's orbit, the intensity of sunlight is I=1.4 kW.m–2 . (This means that 1.4 kW.m–2 passes through 1 square metre at right angles to the sun's rays.) The solar array in the previous question consists of 10 panels, each with area A=1.6 m2 . Under optimal conditions - with the sun at right angles to the array and no clouds in the sky - the array produces Pout=2.3 kW . What is the efficiency of the array? Power out/power in = _____ %.arrow_forwardA parallel-plate capacitor with a plate separation d has acapacitance C0 in the absence of a dielectric. A slab of dielectricmaterial of dielectric constant k and thickness d/ 3 is then inserted between the plates as in Figure P16.61a. Show thatthe capacitance of this partially filled capacitor is given byarrow_forward
- The trace displayed on a CRO screen of a sinusoidal voltage has a peak to peak height of 5.2 V. The root mean square value of this voltage is: A 1.84 V B 2.80 V 2.60 V 5.20 Varrow_forwardProblem #2: Maxwell's Equations. Consider the RC circuit shown. It consists of: an ideal 18 V battery, E a 30 resistor, and a 15 mF capacitor. R The capacitor consists of two circular plates separated by a small distance. Each plate has radius R € 0.46 m. The capacitor is initially uncharged. GH = At time t = 0, the switch is closed. с 3. How fast is the electric flux between the capacitor plates changing at the instant the switch is closed? S 4. When the current through the resistor is 0.40 A, what is the magnetic field at point H, a distance of 0.35 m from the center of the capacitor?arrow_forwardIn the Electric Field Mapping experiment, suppose you used two electrodes separated by a distance L and a power supply with emf Vo Then you measure V for points along a straight line perpendicular to the electrodes, joining the centers of the positive and negative electrodes. You connect the positive terminal of the voltmeter to the anode and the negative terminal to the pointer placed at a point in the tray along the line joining the two electrodes, a distance d from the anode. Which of the following is true? O a. There is a linear relation between Vo and L. b. The slope of V vs. d is negative. C. The slope of V vs. d is positive and depends on Vo only. Od. The positive terminal negative terminal to the point between the two electrodes. the voltmeter should be connected to the cathode and the O e. It is important during the experiment to keep L and Vo fixed.arrow_forward