Fundamentals of Electromagnetics with Engineering Applications
5th Edition
ISBN: 9780471263555
Author: Stuart M. Wentworth
Publisher: John Wiley & Sons
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Chapter 2, Problem 2.71P
A parallel–plate capacitor with a
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A capacitor is made from two flat parallel plates placed 2 mm apart, .and its capacitance at vacuum is 10-12- F , if 200 volt applied in between then a Dielectric material was entered and its Dielectric constant Is 49 , Calculate :
a) the new value of capacitance after the entrance of the Dielectric
b) what is the value of charge on Dielectric material surface
c) the polarization p of the Dielectric material
d) calculate the displacement and the field inside the Dielectric
A ceramic capacitor has an effective plate area of 4 cm2 separated by 0.1 mm of ceramic of relative permittivity 100. Calculate the capacitance of the capacitor in picofarads. If the capacitor in part is given a charge of 1.2 µC what will be the p.d. between the plates?
Two parallel plates of area A=0.01 m^2 are separated by a distance d=5x10^-3 m. The region between these plates is filled with dielectric material of k= 3 and the plates are given equal but opposite charges of 2 micro coulombs. (a) What is the capacitance of this capacitor? (b) Find the potential difference between the plates?
Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 2 - Given P(4, 2, 1) and APQ=2ax+4ay+6az, find the...Ch. 2 - Prob. 2.2PCh. 2 - Prob. 2.3PCh. 2 - Suppose Q1(0.0,-3.0m,0.0)=4.0nC,...Ch. 2 - Prob. 2.5PCh. 2 - Suppose 10.0nC point charges are located on the...Ch. 2 - Four 1.00nC point charges are located at...Ch. 2 - A 20.0nC point charge exists at...Ch. 2 - Prob. 2.9PCh. 2 - Convert the following points from Cartesian to...
Ch. 2 - Prob. 2.11PCh. 2 - Prob. 2.12PCh. 2 - Prob. 2.13PCh. 2 - A 20.0–cm–long section of copper pipe has a...Ch. 2 - A line charge with charge density 2.00nC/m exists...Ch. 2 - You are given two z–directed line charges of...Ch. 2 - Suppose you have a segment of line charge of...Ch. 2 - A segment of line charge L=10.nC/m exists on the...Ch. 2 - In free space, there is a point charge Q=8.0nC at...Ch. 2 - Prob. 2.20PCh. 2 - Sketch the following surfaces and find the total...Ch. 2 - Consider a circular disk in the x–y plane of...Ch. 2 - Suppose a ribbon of charge with density S exists...Ch. 2 - Sketch the following volumes and find the total...Ch. 2 - You have a cylinder of 4.00–in diameter and...Ch. 2 - Consider a rectangular volume with...Ch. 2 - Prob. 2.27PCh. 2 - Prob. 2.28PCh. 2 - Given D=2a+sinazC/m2, find the electric flux...Ch. 2 - Suppose the electric flux density is given by...Ch. 2 - Prob. 2.31PCh. 2 - A cylindrical pipe with a 1.00–cm wall thickness...Ch. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - A thick–walled spherical shell, with inner...Ch. 2 - Prob. 2.37PCh. 2 - Determine the charge density at the point...Ch. 2 - Given D=3ax+2xyay+8x2y3azC/m2, (a) determine the...Ch. 2 - Suppose D=6cosaC/m2. (a) Determine the charge...Ch. 2 - Suppose D=r2sinar+sincosaC/m2. (a) Determine the...Ch. 2 - Prob. 2.42PCh. 2 - A surface is defined by the function 2x+4y21nz=12....Ch. 2 - For the following potential distributions, use the...Ch. 2 - A 100nC point charge is located at the origin. (a)...Ch. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Suppose a 6.0–m–diameter ring with charge...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - The typical length of each piece of jumper wire on...Ch. 2 - A 150–m length of AWG–22 (0.644 mm diameter)...Ch. 2 - Determine an expression for the power dissipated...Ch. 2 - Find the resistance per unit length of a stainless...Ch. 2 - A nickel wire of diameter 5.0 mm is surrounded by...Ch. 2 - Prob. 2.57PCh. 2 - A 20nC point charge at the origin is embedded in...Ch. 2 - Suppose the force is very carefully measured...Ch. 2 - The potential field in a material with r=10.2 is...Ch. 2 - In a mineral oil dielectric, with breakdown...Ch. 2 - Prob. 2.62PCh. 2 - For z0,r1=9.0 and for z0,r2=4.0. If E1 makes a 300...Ch. 2 - Prob. 2.64PCh. 2 - Consider a dielectric–dielectric charge–free...Ch. 2 - A 1.0–cm–diameter conductor is sheathed with a...Ch. 2 - Prob. 2.67PCh. 2 - For a coaxial cable of inner conductor radius a...Ch. 2 - Prob. 2.69PCh. 2 - Prob. 2.70PCh. 2 - A parallel–plate capacitor with a 1.0m2 surface...Ch. 2 - Prob. 2.72PCh. 2 - Prob. 2.73PCh. 2 - Given E=5xyax+3zaZV/m, find the electrostatic...Ch. 2 - Suppose a coaxial capacitor with inner radius 1.0...
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- A ceramic capacitor is to be constructed to have a capacitance of 0.01µF and to have a steady working potential of 2.5 kV maximum. Allowing a safe value of field stress of 10 MV/m, determine (a) the required thickness of the ceramic dielectric, (b) the area of plate required if the relative permittivity of the ceramic is 10, and (c) the maximum energy stored by the capacitor.arrow_forwardTwo concentric cylindrical plates have an outer radius of 4 cm, an inner radius of 3.8 cm, and a cylinder length of 10 cm. The gap of both plates contains air. Specify: a. Capacitance of capacitors (in pF, pico-farad). b. Capacitor charge (in nC, nano-coulomb) if the capacitor is connected to a 12 volt power source. c. Capacitance and charge captor if the gap of both plates is filled by the material with a dielectric constant of 2.3.arrow_forwardA parallel-plate capacitor consists of square plates of edge length ℓ that are separated by a distance d, where d << ℓ. A potential difference ΔV is maintained between the plates. A material of dielectric constant k fills half the space between the plates. The dielectric slab is withdrawn from the capacitor as shown. (a) Find the capacitance when the left edge of the dielectric is at a distance x from the center of the capacitor. (b) If the dielectric is removed at a constant speed υ, what is the current in the circuit as the dielectric is being withdrawn?arrow_forward
- A parallel plate capacitor contains two dielectrics A and B (interfaces parallel to E and D) with relative permittivity of 1.5 and 3.5 respectively. Dielectric B comprises one third of the capacitor's volume and the remaining volume is occupied by dielectric A. If the area of each conducting plate is 3 square meters and the separation between them is 2 mm, find the capacitancearrow_forwardTwo identical capacitors in series with plate area A and between plates d are connected to a constant voltage DeltaV = 10V as shown in Figure 1. After the capacitors are fully charged, the switch is opened and the dielectric constant k = 4.0, thickness d and surface area A/2 are placed. Accordingly, what is the potential difference (Vb-Va) between the terminals of the capacitors in volts?arrow_forwardA parallel plate capacitor has an area of 7.45 × 10−4?2and its plates are separated by a distance of 2.45 ?? across which a potential of 20 ? is applied. If a material with dielectric constant 6 is introduced between the plates, determine the capacitance, the charge stored on each plate, the dielectric displacement and the polarization.arrow_forward
- A parallel-plate capacitor using a dielectric material having an Pr of 2.2 has a plate spacing of 2 mm (0.08 in.). If another material having a dielectric constant of 3.7 is used and the capacitance is to be unchanged, what must the new spacing be between the plates?arrow_forwardA capacitor sensor of three parallel plates, having distance between upper plate and middleplate is 0.75cm and the distance between lower plate and middle plate is 0.46cm, having an areaof 28mm. Due to displacement, if upper plate and lower plate are moved towards the middleplate by 3mm, then calculate the following,i. Capacitance between upper and middle plates.ii. Capacitance between lower and middle plates. iii. Net capacitance of the capacitor sensor.arrow_forward3. A ceramic capacitor has an effective plate area of 5cm2 separated by 0.1mm of ceramic of relative permittivity of 100. Calculate the capacitance in microfarads. If the capacitor is given a charge of 1.5 µC what will be the potential difference (pd) between plates? & calculate the energy stored in itarrow_forward
- A capacitor is formed from a pair of long concentric cylinders with radius 4 mm and 8 mm, and with a dielectric of relative permittivity of 5 in between the conducting cylinders. The voltage at the inner cylinder is 90 V and the voltage at the outer cylinder is 0 V. a) Calculate V, E, and D between the two conductors at radius 6 mm. b) Calculate ρs, the surface charge density in Coulombs/m2 on each cylinder. Please solve for Ps, for each cylinder. Thank you very much. Please be careful while inserting the values.arrow_forwardThe space between the plates of a parallel plate capacitor of area A is occupied by two blocks of dielectric material, one with constant K1 = 2 and the other with constant K2 = 3. The thickness of each block is the same as the spacing d = 1mm between the plates, and each one fills half the volume between them. Determine the capacitance at the ends if the area of plates is 2 m^2arrow_forwardCalculate the energy stored in a parallel-plate capacitor which consists of two metal plates, each 60cm2 separated by a dielectric 1.5mm thick and of relative permittivity 3.5 if a p.d. of 1000 v is applied across it.arrow_forward
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