Engineering Electromagnetics
Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 8, Problem 8.26P
To determine

(a)

The value ofa.

To determine

(b)

The value ofa.

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Consider 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.
Two ideal solenoids of radii R and 4⁢R , respectively, have n turns per meter, and each carries a current of I. Both currents flow in the same direction. The small‑radius solenoid is placed inside the large-radius solenoid so that their axes of symmetry are parallel and separated by a distance d=2⁢R . Neglecting any magnetic screening effects, express the magnetic field strength on the axis of the small-radius solenoid analytically in terms of the quantities given and the magnetic permeability of a vacuum, μ0 .
Consider a long wire in the air (a thin perfectly conducting cylinder ofinfinite length) of radius r0 and charge per unit length q Cm−1.(a) State Gauss’ law for the electric flux density D.(b) The electric flux density D outside the wire varies with the radial distance rfrom the center of the wire. Use Gauss’ law to calculate the electric flux density Das a function of r for r larger than the radius of the wire.(c) What is the equation relating electric field E to electric flux density D in air?What is the electric field E as a function of r for r larger than r0?(d) Suppose we measure voltages relative to a point g outside the wire that is a radialdistance rg from the center of the wire. Write down an integral for the voltage V ofthe wire relative to the point g.(e) The capacitance of the wire per unit length is defined as q/V . If the radius r0of the wire increases, how does the capacitance per unit length change? Explain.

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Engineering Electromagnetics

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