Problem (3): If the electric field is defined as: E(Đ) = sin(60) Ý, ( Eo cos(3wt²) x, t≥ 3 t<3 = 1/π? Find the displacement current density at t=0 and t = π/3, where w =
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- A (1.215x10^0)-m radius cylindrical region contains a uniform electric field along the cylinder axis. It is increasing uniformly with time. What is the rate of change (magnitude) of the electric field required to obtain a total displacement current of (4.64x10^0) nA through a cross section of the region? Provide your answer in V/(m.s) with three significant figures.For a spherically symmetric volume of charge in a vacuum with a charge density that is given by: Pv = Qe™ for 0 a %3D Find the Displacement Current Density vector for r < a if the charge distribution is in a material with a dielectric constant that is er. (Q/r2)[In(b) - In(a)] ar -(Qea/r2)[1/a + 1/a²] ap -[QaaIn(a)][a? + 2a +2] ar O ar -(Qe" )(1 + 2/r + 2/r2) a r (-Qeª/r²) arPs Two Conductancas G ard 62 haring valnes of b0o and Joo yn S respectiny , are connactid in pavallil. The Combination is then Gonmeetid in parallal with 800 resistor. Calculate the s a) Eguiralant re wistanca ofthe parallal Circnit. [Ans: 363. 6352 b) Curant in each branch if Gq Carries 2mA. Ans: SA 4.16 m power diss ipatid in coah draned. [Anso 6.6mw,lomw13-8mm d) Voltage across each omponant-LAnse 3.33. e) Total power dissipatol-(Ans: 30.5 mn). Pt A 6v battey, delivers loMA to thvee vesistors in faralkel , R, 21kr, R2=2k2,R3=Rx. Caleulatas a) Curront in Rx sthat is Ix. [Anss I mÁ) b) Power dissipatid. by Rx and Ry-{Anss 6mw, 36 mm. C) Resistance vatio Rx/R--(Anst 615). d) Cuvrent vatio Ji/Ix- [Anss 6/4]-
- In a medium with (μ, = 1,6,= 8) the electric filed intensity is given by E = 10 sin(1000t - 10x) ay V/m. Calculate the displacement current density.A 1.212 m radius cylindrical region contains a uniform electric field along the cylinder axis. It is increasing uniformly with time. What is the rate of change (magnitude) of the electric field required to obtain a total displacement current of 3.21 nA through a cross-section of the region? The answer should be in V/(m.s) with three significant figures.The parallel plates of transmission line having dimensions b = 4cm and d = 8mm while the medium between plates is characterized by µR = 1, ɛR =1 and ơ = 0.Given the field H = 5cos (10 9 t - βz)ay. Use Maxwells equation to compute displacement current density at z = 0.
- Consider a rectangular pipe with dimensions (Ax, Ay, Az), with insulating sidewalls (located at +Ax/2) and conducting top/bottom walls (located at ±Ay/2). Ionized, conducting plasma flows through the pipe with velocity v= v, î, and a uniform magnetic field is imposed: B = B, î. %D (a) What is the potential between the top and bottom walls of the pipe? (b) If the top and bottom walls are connected by a load resistance R, and the plasma has conductivity o, how much current is driven through the load?Figure 1. illustrates a parallel-plate capacitor of radius 3 cm, made of lossy dielectric material with ɛ, 74ɛ, and conductivity of 5 S/m. Assuming the V(t) = 10 sin wt, calculate the conduction current in the parallel-plate сарacitor. + V(t) E, o 5 cm Figure 1: parallel-plate capacitorApplication of Curl 2. Calculate the value of the vector current density: (a) in rectangular coordinates at PA(2, 3, 4) if H = x Zzay-y2xaz; Application of Stokes Theorem 3. Evaluate both sides of Stokes' theorem for the field H=6xyax-3y2ay A/m and the rectangular path around the region, 2 ≤x≤5, -1sy≤ 1,2=0. Let the positive direction of d5 be az
- The electric field strength in the region 0do P(0,0.2) R FIGURE 3-11 A uniformly charged disk (Example 3-8).Problem 2 Show that in a current-free volume of space, a static magnetic field can never have a local maximum by considering V(B· B) · da, where S is the surface of a small volume V containing a point P in space.SEE MORE QUESTIONS