Concept explainers
Consider a composite material made up of two species: having number densities N1 and N2 molecule s/m3, respectively. The two materials are uniformly mixed, yielding a total number density of N = N1 +N2- The presence of an electric field E induces molecular dipole moments p1 and p2 within the individual species, whether mixed or not. Show that the dielectric constant of the composite material is given by
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Engineering Electromagnetics
- A dipole is composed of a pair of point charges ±?, separated by a distance ?d and aligned parallel with the ?-x-axis, as shown in the figure. Find the expression for the potential ? on the ?-axis at point F located at ?=3.77×10−8 cm, where ?≫?. Then, evaluate the potential for a dipole moment of ?=8.00×10−30 C·m. The Coulomb force constant is ?=1/(4??0)=8.99×109 N·m2/C2.arrow_forwardA charge QA = 30μC is located at A(2, 1, 4), and a charge QB =50μC is at B(5, 8,−2) in free space. If distances are given inmeters, determine the electric field intensity at point C( -2, 3, 1).arrow_forwardA dipole having a moment p = 3ax − 5ay + 10az nC · m is located atQ(1, 2,−4) in free space. Find V at P(6, 3, 4).arrow_forward
- The polarization vector in a dielectric tube of inner radius ri and outer radius ro is ?⃗ = ?0(?̂?2? + ?̂?3?). Theaxis of the dielectric tube defined by z0>z>0 coincides with the z-axis. a) Determine the equivalent polarization surface and volume charge densitites. b) Show that the total bound charge is zero.arrow_forwardDesign a dielectric-filled rectangular waveguide for transmission of electromagnetic power at 2.45 GHz. Find the maximum power the waveguide can transmit. Use an electric field safety factor of 10. Neglect conduction losses. The material filling the waveguide is nonmagnetic with zero conductivity, and has r = 2.1; its breakdown electric field is 6x107 V/m.arrow_forwardAn electric dipole located at the origin in free space has a moment p = 3ax - 2ay+az nC · m. Find V at P(2, 3, 4)arrow_forward
- Coaxial conducting cylinders are located at ? = 0.5 cm and ? = 1.2 cm. The region betweenthe cylinders is filled with a homogeneous perfect dielectric. If the inner cylinder is at 100 V and the outer is at 0V, find(a) the location of the 10 V equipotential surface;(b) the maximum value of electric field ( ????? );(c) the dielectric constant of the medium (??), if the charge per meter length on theinner cylinder is 10 nC/m.arrow_forwardIn free space ⃗?⃗ (?, ?) = 70cos(?? − ??)⃗?⃗ (V/m). Find the average power crossing a circular area of radius 2 meters in a plane ? = 0.arrow_forwardExample: A 31/4dipole is radiating into free-space. Input power to the dipole is 100 W. Assuming an overall efficiency of 50%, find the power density (in W/m?) at (r = 500 m, 8 = 60°, ¢ = 0)? Solution:arrow_forward
- Calculate the wavelength for an electron in the first orbit in the hydrogen atom, and the wavelength for an electron having a velocity of 1200km/s then compare the resultsarrow_forwardConsider the dipole in the figure below with the charge magnitude of q = 3.0 nC and separation distance d = 4.0 cm. What is the potential at the following locations in space? (a) (0, 0, 1.0 cm); (b) (0, 0, –5.0 cm); (c) (3.0 cm, 0, 2.0 cm).arrow_forwardcan you please solve this question, thanks. A sheet of charge, m , is present at the plane x = 3 in free space, and a line charge of rL = 20 nC/m , is located at x = 1, z = 4. (a) Find the magnitude of the electric field intensity at the origin. (b) Find the direction of E at P(4,5,6)arrow_forward
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