Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 8, Problem 8.5P
To determine
The torque on cylinder.
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A flat, circle surface area with a radius of 4m is in the YZ-plane at x=0, Find the magnitude of the magnetic flux through this surface produced by a magnetic flux density of B=3.5ax-6.4ay+8az T
a) A circular loop of radius ? carries current ? as shown in the figure. Find the magnetic flux density ?⃗ at a point on the axis of the loop by using Biot-Savart law. Show all the details of Biot-Savart formulation b) A surface charge density exists on the hemispherical surface of the radius ? shown in the figure given as??⃗⃗ =?0????ê?A/m where ?0 is constant. i) Find the total current flowing on the surface ii) Using the solution of part (a), find the magnetic flux density ?⃗ at the origin ?.
Consider an infinitely large sheet lying in the xz-plane at the origin, the extent of the sheet in thex, and z direction is infinite. The sheet carries surface current J = J0ˆk, where J0 is the current per unit width perpendicular to the flow. Calculate the magnetic field everywhere (y > 0 and y < 0) due to J. Sketch the Amperian loop.
Chapter 8 Solutions
Engineering Electromagnetics
Ch. 8 - A point charge, Q = - 0.3 /C and m = 3 Ă— -10-16...Ch. 8 - Prob. 8.2PCh. 8 - Prob. 8.3PCh. 8 - Show that a charged particle in a uniform magnetic...Ch. 8 - Prob. 8.5PCh. 8 - Show that the differential work in moving a...Ch. 8 - A conducting strip of infinite length lies in the...Ch. 8 - Two conducting strips, having infinite length in...Ch. 8 - A current of-100az A/m flows on the conducting...Ch. 8 - A planar transmission line consists of two...
Ch. 8 - Prob. 8.11PCh. 8 - Two circular wire rings are parallel to each...Ch. 8 - An infinitely long current filament is oriented...Ch. 8 - A solenoid is 25 era long, 3 cm in diameter, and...Ch. 8 - Prob. 8.15PCh. 8 - Prob. 8.16PCh. 8 - Prob. 8.17PCh. 8 - Prob. 8.18PCh. 8 - Given a material for which ℵK = 3.1 and within...Ch. 8 - Find H in a material where (a) fir = 4.2, there...Ch. 8 - Prob. 8.21PCh. 8 - Prob. 8.22PCh. 8 - Calculate values for HO,B0, and M0 at p = c for a...Ch. 8 - Two current sheets, K0,ay, A/m at z = 0 and -K0,ay...Ch. 8 - Prob. 8.25PCh. 8 - Prob. 8.26PCh. 8 - Let đ�œ‡rj = 2 in region 1, defined by 2x + 3y —...Ch. 8 - For values of B below the knee on the...Ch. 8 - Prob. 8.29PCh. 8 - Prob. 8.30PCh. 8 - A toroid is constructed of a magnetic material...Ch. 8 - Prob. 8.32PCh. 8 - Prob. 8.33PCh. 8 - Determine the energy stored per unit length in the...Ch. 8 - Prob. 8.35PCh. 8 - Prob. 8.36PCh. 8 - A Toroid has known, reluctance R. Two windings...Ch. 8 - Prob. 8.38PCh. 8 - Conducting planes in air at Z = 0 and z = d carry...Ch. 8 - Prob. 8.40PCh. 8 - Prob. 8.41PCh. 8 - Find the mutual inductance between two filaments...Ch. 8 - Prob. 8.43PCh. 8 - Prob. 8.44PCh. 8 - Beginning with the definition, of the scalar...
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- The magnetic flux density in all of space is given by B=(3z)ax+(8x2−x2y)ay+(y+x2z)az Wb/m2. Let S denote the paraboloidal surface defined by y=x2+z2,0≤y≤64. Find the net magnetic flux Φ passing through S in the direction away from the xz-plane. Hint: Think about whether there is another way to solve this, such as by using a capping surface.arrow_forwardA steady current ? flows down a long cylindrical wire of radius ?. Find the magnetic field both inside and outside if,a) The current is uniformly distributed over the outside surface of the wire. b) The current is distributed in such a way that ? is proportional to ?, the distance from the axis. check the image, explain step by step.arrow_forwardIn the figure, an electron accelerated from rest through potential difference V1=1.15 kV enters the gap between two parallel plates having separation d = 22.2 mm and potential difference V2= 187 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?arrow_forward
- Q1) Evaluate both sides of stoke's theorem if the magnetic flux density is given by 37.7r aphi(vector) uWb/m^2 in a free space area defined byr = 3; 0arrow_forwardThe flux density within the cylindrical volume bounded by r = 5m, z = 0 and z = 2 m is given by, D=30 eta-2 z a, C/m². what is the total outward flux crossing the surface of the cylinder?arrow_forwardThe magnetic flux density in a region of free space is given as B = ?3x ax + 5y ay ? 2z az T. Find the total force on therectangular loop shown in Figure 2 if it lies in the plane z = 0 and is bounded by x = 1; x = 3; y = 2 and y = 5, all thedimensions are in cm.arrow_forward
- An infinitely long wire carrying current is extended along the z-axis. A square plate with edge length a, lying in the yz plane, is placed next to the wire. Find the magnetic flux passing through the plate surface.arrow_forwardSupposed that a coaxial cable consists of a solid inner conductor of radius a, surrounded by a concentric cylindrical tube of inner radius b and outer radius c as shown below. We assume that the conductors are carrying an equal current I naught that is distributed equally into the cross-section but of different directions as indicated by the directions in the image above. Calculate the magnitude of magnetic field at a distance r from the axis, where: - rc Plot the magnitude of the magnetic field with respect to the distance r from the axis.arrow_forwardConsider an infinitely long wire in the form of y2=4cx, which is in a stationary state. Another infinitely long wire parallel to the y-axis starts moving with an initial velocity of zero at t=0 from the initial position at x=0 with acceleration a ax. Assuming a magnetic flux density (magnetic induction) of B=B0 az throughout the region, determine the induced electromotive force on the moving wire as a function of time using Faraday's law.arrow_forward
- A circular loop of radius a, centered at origin and lying in the xy plane, carries current I as shown in the figure.The magnetic field intensity a the centre of the loop will bearrow_forwardThe electric field present in the region is given by the expression shown in the photo in V/m. Determine the amount of flux, in pC, passing through a disk of radius 5m. The said disk lies on the plane z=2marrow_forwardConsider two coaxial solenoids with free space cores. Solenoid A is placed inside Solenoid B and solenoid B carries a current of 2I0 which creates a magnetic flux density of magnitude of B0. If the cross-sectional area, length and number of turns per length of Solenoid A are S, 4h and n respectively, calculate the mutual inductance between Solenoid A and Solenoid B.arrow_forward
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