Concept explainers
Let đ�œ‡rj = 2 in region 1, defined by 2x + 3y — 4z >1, while pr2 = 5 in region 2 where 2x + 3y - 4z < 1. In region 1, H1 = 50ax - 30ay + 20az A/m. Find (o) HM1; (b) Hr1 (c)Hr2; (d) HN2 (e) 01, the angle between H1 and aN2; (f) 02, the angle between H2 and aN2].
(a)
The value of
Answer to Problem 8.27P
The required value is,
Explanation of Solution
Given Information:
The region 1 is
Calculation:
Both regions are separated by the surface
So, the normal component of magnetic field intensity:
Conclusion:
The required value is,
(b)
The value of
Answer to Problem 8.27P
The required value is,
Explanation of Solution
Given Information:
The region 1 is
Calculation:
The tangential component of magnetic field intensity:
Conclusion:
The required value is,
(c)
The value of
Answer to Problem 8.27P
The required value is,
Explanation of Solution
Given Information:
The region 1 is
Calculation:
The tangential components of magnetic field intensity are continuous across the surface between the regions. So:
:
Conclusion:
The required value is,
(d)
The value of
Answer to Problem 8.27P
The required value is,
Explanation of Solution
Given Information:
The region 1 is
Calculation:
The normal components of magnetic flux density are continuous across the surface between the regions. So,:
Conclusion:
The required value is,
(e)
The angle between
Answer to Problem 8.27P
The angle between
Explanation of Solution
Given Information:
The region 1 is
Calculation:
The unit normal vector:
The required angle:
Conclusion:
The angle between
(f)
The angle between
Answer to Problem 8.27P
The angle between
Explanation of Solution
Given Information:
The region 1 is
Calculation:
The unit normal vector:
The magnetic field intensity:
The required angle,
Conclusion:
The angle between
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Chapter 8 Solutions
Engineering Electromagnetics
- In a spherical electrode system, gas material with the most favorable arrangement in terms of puncture resistance, outer radius r2 = 3.2 cm, puncture field strength Ed=75kV/cm and dielectric constant Ergas=1 is used. According to this;a) Calculate the inner radius of the electrode and the puncture voltage of the system according to the geometrical characteristics of the most suitable arrangement in terms of puncture resistance.b) Draw the puncture curve in the p-Emax plane for a voltage of U=40kV provided the outer radius is kept constant and indicate the boundaries of the inner sphere radii on the curve.c) Briefly interpret the electrode system in terms of discharge events in the geometric characteristics of p=0.8, p=1.8 and p=5 on the puncture curve.arrow_forwardA 132kV line with 1.956 cm diameter polished conductors is built so that corona takes place if the line voltage exceeds 97kV per phase. If the value of potential gradient at which ionization occurs cab be taken as 32kV (Max) per cm and air density factor = 0.91. The spacing between the conductors isarrow_forwardThe outside diameter of a concentric spherical electrode system is given as 28 cm. The system is the most suitable sized according to puncture. Puncture strength of gas between spherical layers, Ed = 88 kV / cm and the relative dielectric constant of the gas is r1 = 1 a) Calculate the capacity of the system and the highest voltage at which the system can be punctured. what should be. b) For U = 180 kV execution case, the maximum and minimum occurrence on the system electric field calculation addition? (Ɛ0 = 8,854x10-12 F / m)arrow_forward
- In a three layered, cylindrical electrode system, 100 kV is applied to the inner conductorwhile the outer conductor is grounded. Radii of cylinders in this system are: r1 =1 cm, r2 =1.5cm, r3 =3 cm, and R =5 cm. Relative dielectric constants of layers are r1 = 5, r2 = 3 and r3 =2.5 respectively;a) Calculate maximum and minimum field strengths across each layer.b) If R=5 cm and r3 =4.5 cm, for uniformly stress condition find the new values of r1 and r2and the thickness of each layer.arrow_forwardIt is viewed from the cross-section of a coaxial cable consisting of a cylindrical conductive tube with an internal radius R and an outer radius of Rz wrapped around a cylindrical conductive wire with a RADIUS of R. r to indicate the radial distance from the center, the inner cylindrical conductor,if it is j1 = Gr and the outer conductive tube, j2 = Car has improper current densities. Here, the two conductors carry the same I flow in zit directions. What is the size of the B2 magnetic fields at r=1 cm and B2 at r= 8 cm?(R=4 cm; R=7 cm, R3=9 cm; Io=2 A; uo=47.10-7 T.m/A and our aquani-positive forehead outward from the page plane).arrow_forward96 kg of ice has accumulated over 40 meters of a conductor whose 40 meters are 46 kg in a naked state. This conductor is III, where k=0.3. is in the ice zone.Since it is known that it is calculated with qb=k√d (kg/m) and the conductor is exposed to wind force at the same time with ice on it, calculate the q+bw value as kg/m.Frosted diameter D=√d2+216.46 qb mm (d bare conductor diameter, qb ice load in kg/m)Wind load qw=p x d x c x 10-3 N/m (no ice condition, different formula will be used in icy condition.)It will be taken as c=2 and p=294.3 N/m2arrow_forward
- Q1: a- find the area of the following surface r=4 , π/4<θ<2π/3 ,0<φ<π b- find the volume of the following region 4<ρ<5 ,π/3<φ<π ,-2<z<2 Q2: Given F ⃗=2xya ̂_x+(x^2-z^2 ) a ̂_y-3xz^2 a ̂_z Find the line integral ∫_A^B▒〖F ⃗.(dl) ⃗ 〗 from A(0,0,0) to B(3,2,4) along the segments (0,0,0) to (0,2,0) to (3,2,0) to (3,2,4)arrow_forwardHigh Voltage Technique For the most puncture-related arrangement of a concentric spherical electrode system with a voltage of 100 kV to be applied between the electrodes and with Ed=80 kV/cm (insulator puncture strength), Emax = 0.6. Ed a) Inner and outer sphere radii, b) Maximum and minimum field strengths, c) Equivalent electrode opening and utilization factor, d) Its capacity (Ɛ0=8,854x10-12 F/m, Ɛr=1) and insulator volume, e) By keeping the outer sphere radius constant, calculate the inner sphere radius value range that can be used in the system without discharge. ANSWERS: a) r1=4.16 cm, r2=8.32 cm b) Emax=48 kV/cm, Emin=12 kV/cm c) α=2.08 cm, η=0.5 d) C=9.257 pF, Vinsulator=2110 cm3 e)1.53<r1<6.8 cmarrow_forwardThe outer radius of a concentric spherical electrode system is given as 20 cm. The system is the most suitable sized according to puncture. Puncture strength of gas between spherical layers Ed = 80 kV / cm and the relative dielectric constant of the gas is r1 = 1. 0) - Calculate the capacity of the system and the highest voltage that can be applied to the system without puncture Determine what should happen. b) - For the case of U = 100 kV application, the maximum and minimum occurrence on the system Calculate the electric field values? (Ɛ0 = 8,854x10-12 F / m)arrow_forward
- A 200 mm square single core copper conductor cable operating at 22kV, 50Hz has the following parrameters: external diameter of insulation, do = 73,5mm, diameter of conductor including area , di = 28,5mm. Calculate the dielectric loss of 1km length of cable if: I) The cable insulation is XPLE with er= 2,5 and tanr= 0.0003arrow_forwardThe relative dielectric coefficient of the planar electrode system given in the figure is Er = Er0 - n. It changes linearly according to the x relation. Er0 = 7.2 for this electrode system; n = 1.8 cm ^ -1 and the gap between electrodes is given as a = 3 cm. 26 kV direct voltage is applied to this planar electrode system, so find the amplitude of the electric field strength at point A (2.7cm, 3cm). (Edge effects will be neglected, electrode length b <15 cm) y 4 a (cm) -> electrode electrodearrow_forwardConsider region 1 (z<0) contains a dielectric for which ϵr=2.5, and region 2 (z>0) is characterized by ϵr=4 .Let E1=−30ax+50ay+70az V/m. The D2 is given byarrow_forward
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