Concept explainers
Construct a curvilinear- square map of the potential field between two parallel circular cylinders, one of 4 cm radius inside another of 8 cm radius. The two axes are displaced by 2.5 cm. These dimensions are suitable for the drawing. As a check on the accuracy, compute the capacitance per meter from the sketch and from the exact expression:
Where a and b are the conductor radii and D is the axis sepatation.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Loose Leaf For Engineering Electromagnetics
- 3.(Part I) A 50 V voltage generator at 20 MHz is connected to the plates of an air dielectric parallel-plate capacitor with a plate area of 2.8 cm^2 and a separation distance of 0.2 mm. Find the maximum value of displacement current density and displacement current. (Part II) A dielectric material with permeability that of free space, permittivity = 9xpermittivity of free space, conductivity = 4 S/m, is placed between the plates of a parallel-plate capacitor. Calculate the frequency at which the conduction and displacement currents are equal.arrow_forwardFind the capacitance of a cylindrical capacitor with length of 45 cm, inner radius of 6 mm, and outer radius of 9 mm. The relative permittivity of the medium is 8.87arrow_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 The dielectric slab is withdrawn from the capacitor as shown.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 (b) If the dielectric is removed at a constant speed υ, what is the current in the circuit as the dielectric is being withdrawn?arrow_forward
- Given the potential field in cylindrical coordinates, V = 100 + 50ρ + 150ρ sinΦ volts, and point P at ρ = 1 m, Φ = 600, z = 0.5 m, find the electric field intensity E at P.arrow_forwardA cylindrical capacitor is made of two concentric conducting cylinders. The inner cylinder has radius R1 = 19 cm and carries a uniform charge per unit length of λ = 30 μC/m. The outer cylinder has radius R2 = 25 cm and carries an equal but opposite charge distribution as the inner cylinder. a. Use Gauss’ Law to write an equation for the electric field at a distance R1 < r < R2 from the center of the cylinders. Write your answer in terms of λ, r, and e0. E= b. Write an equation for the energy density due to the electric field between the cylinders in terms of λ, r, and e0. u = c. Consider a thin cylindrical shell of thickness dr and radius R1 < r < R2 that is concentric with the cylindrical capacitor. Write an equation for the total energy per unit length contained in the shell in terms of λ, r, dr, and ε0. dU/l = d. Calculate the energy stored per unit length in the capacitor in units of joules per meter. U/l = e. Calculate the electric potential difference between…arrow_forwardFor a solenoid (toroidal inductor), the inductance (L) could be increased because of:1, The number of turns of wires (N) is increased2, The cross-sectional area of the toroid (A) is decreased3, the length of the wire used to wrap the toroid (l) is decreased4, the relative permeability of the core material (r) is larger(single answer)1, 2, 43, 41, 21, 31, 3, 41, 2, 3arrow_forward
- 27. A phasor can be represented or expressed in either rectangular form (x +j y) or polar form (z cis n) True False 28. By convention, values obtain from time domain representation are always real while in phasor domain representation, values are generally expressed in complex form. True False 31. Value of capacitance is usually affected by the following physical dimensions and construction of a capacitor: such as number of turns, its length, its cross-sectional area and the permeability of the core. True Falsearrow_forwardDetermine the total potential energy, in microjoules, stored in a parallelepiped of dimensions are 9 m by 6 m by 8 m if the electric field inside is given as E = 17 ar + 19 aθ + 15 aϕ V/m. Use the permittivity of free space as 8.854 × 10-12 F/m.Ans: 1.6734If the electric field in the region is given as E = -cos(θ) sin( 4 Φ) aθ + b cos( 4 Φ) aφ V/m. Determine the potential at point A(4 m, 0.46 rad, 2.07 m), in volts, if the potential at point B(4 m, 1.00 rad, 0.10 m) is 60 volts. The value of b is also the coefficient of Φ.58.4552 Compute for the potential difference, in volts, in moving a charge from A(3, 2, -2) m to B(7, -6, 6) m against the electric field due to a disk charge of radius 9 m on the plane x = 0. The disk has a total charge of 9 nC. Ans: -18.7657arrow_forwardA 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?arrow_forward
- The capacity of a full cylindrical capacitor of length L with inner radius a and outer radius b, C = (2πϵrϵo)*L / (ln (b / a))is known to be. The capacitor is angularly composed of two insulating regions and these insulating regions are; With ø1 = 2.3 rad and a region with a relative dilutive constant εr1 = 5.6 Regions with relative dilutive constant ø2 = 3.9831 rad r2 = 3.2 The equivalent capacity of this capacitor is how many times the capacitor whose insulator is the space. (ø2 + ø2 = 2π) The gap dielectric constant εo = 8.842 pF / m and capacitor dimensions; L = 20 cm a = 1.5 cm b = 3.4 cmarrow_forwardIn empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient Er = 7 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: Electric field vector at (x <x1) E1 = (6.5)ux + (0.5)uy+(7.5)uz has been observed.Region II : The relative dielectric constant at (x1 <x <x2) is r = 7.Region III: By determining the electric field E3 at (x2 <x) (space er = 1),|E3| write its value numerically.arrow_forwardSHOW YOUR COMPLETE SOLUTION, MAKE SURE YOUR ANSWERS ARE IN 4 DECIMAL PLACES. A uniform line charge ρL = 15 nC/m lies on the line, x = -6, z = 8, in freespace. Find E in the Cartesian components at:(a) originarrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,