For the following vector magnetic potential in the phasor representation, A(R, 0) = a Нот 4πR² (1+jBR)e-jẞR sin 0, where μo,m, and ẞ are the related particular constants, calculate: a) the associated magnetic field by using the solenoid attribute of the magnetic field, b) the relevant electric field by using Maxwell's equation in phasor forms.
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A: The given values are, ϕ=0.553 V·m/srRtR=3.50 cm=0.035 m
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A: We can verify this by writing the four Maxwell's equation.
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A: (a) Use Maxwell’s third equation ∂E∂x=-∂B∂t=-∂∂t12μoJmaxsinkx-ωt=ω2μoJmaxcoskx-ωt
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A: Basic Details The displacement current can be determined as the product of permittivity of free…
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A: The given electric field vector is
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A: a) The expression is for Electric field is,
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Q: a) A uniform field pointing directly out of the page is present in a circular region and steadily…
A: Rather than using maxwells equations directly, we will look at the concepts from which maxwells…
Q: The magnitude of the electric field between the two circular parallel plates in the figure is E =…
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Q: In the figure an electric field is directed out of the page within a circular region of radius R =…
A: This problem can be solved using Ampere maxwell law.
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Q: A mass spectrometer is used to separate uranium ions of mass 3.92 *10-25 kg and charge 3.20 * 10-19…
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- As a parallel-plate capacitor with circular plates 20 cm in diameter is being charged, the current density of the displacement current in the region between the plates is uniform and has a magnitude of 20 A/m2. (a) Calculate the magnitude B of the magnetic field at a distance r = 50 mm from the axis of symmetry of this region. (b) Calculate dE/dt in this region.Problem (1): A circular parallel plate capacitor was charged by a battery with a potential difference AV, the resulting magnetic field of the capacitor at any distance r from the plate center is given by: HOAV e-t/RC| 2nR Where R is the wire resistance of the circuit, ro is the plate radius, C is the capacitance. Use this information to find the displacement current density between the capacitor plates?The figure shows a circular region of radius R = 3.00 cm in which an electric flux is directed out of the plane of the page. The flux encircled by a concentric circle of radius r is given by OE,enc = (0.714 V-m/s) (r/R)t, where r ≤ R and t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a)2.00 cm and (b)7.00 cm? (a) Number i 2.81E-17 (b) Number 1.81E-17 Units Units T T R
- A cylindrical magnet has a cross sectional radius of 1.68 cm. The magnitude of the magnetic field produced by this magnet is represented by the equation B = a + b cos(wt + p) where a = 35.0 T, b = 0.395 T, and w = 60 rad/s. (a) Find the maximum value of the induced electric field at a distance of 1.46 cm from the axis of the cylindrical magnet. V/m (b) Find the maximum value of the induced electric field at a distance of 1.90 cm from the axis of the cylindrical magnet. V/mIn the figure an electric field is directed out of the page within a circular region of radius R = 3.50 cm. The magnitude of the electric field is given by E (0.800 V/m.s)(1 - r/R)t, where radial distance r≤R and t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a)2.50 cm and (b)7.50 cm? R (a) Number i 3.2767933E-21 Units T (b) Number i 1.513724E-20 Units T > >You are given a VHF television antenna (the antenna type is a magnetic loop antenna) and asked to determine the signal strength going into the reciver from the antenna. The antenna is a circular 1-turn loop of diameter 12.9 cm. The magnetic field of the TV signal is perpendicular to the plane of the loop, and is essentially uniform over the area of the loop at any given instant. If the magnetic field is given by B = Bosin(2*pi*f*t) where Bo = 6.9 nT and f = 258.8 MHz (megacycles/sec), the maximum value of the emf induced in the loop,Emf , is the strength of the signal going into the reciver in mV. What is this signal strength of Emf ?
- In the figure, a long, straight copper wire (diameter 2.46 mm and resistance 0.807 2 per 250 m) carries a uniform current of 25.0 A in the positive x direction. For point P on the wire's surface, calculate the magnitudes of (a) the electric field E, (b) the magnetic field B, and (c) the Poynting vector 3, and (d) determine the direction of S. y P (a) Number i (b) Number i (c) Number (d) -Y i Units V/m Units T Units W/m^An electric field with initial magnitude 130 V/m directed into the page and increasing at a rate of 13.0 V/(m · s) is confined to the area of radius R = 15.0 cm in the figure below. If r = 46.0 cm, what are the magnitude and direction of the magnetic field at point A?Problem 5. As a parallel-plate capacitor with circular plates 20 cm in diameter is being charged, the displacement current density in the region between the plates is uniform and has a magnitude of 20 A/m². (µ₁ = 4×10−7 T·m/A, and &o = 8.85x10-¹2 C²/N·m²). (a) Calculate the magnitude B of the magnetic field at a distance r = 50 mm from the axis of symmetry of this region. (b) Calculate dE/dt in this region.
- A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 × 10-25 kg and charge 3.20 × 10-¹⁹ C from related species. The ions are accelerated through a potential difference of 122 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.03 m. After traveling through 180° and passing through a slit of width 0.923 mm and height 1.19 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 1.17 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.15 h. (a) Number i (b) Number (c) Number MO i Units Units Units -DetectorHo Idlxf 4π 72 dB This problem checks your understanding of the term in the equation for the magnetic field due to a small "piece" of current, Consider a small piece of current (perhaps there's a wire) at location $ whose coordinates are (6 m, 2 m, 10 m). We would like to find the magnetic field at location P whose coordinates are (2 m, 5 m, 2 m). The term " is the distance between point S and point P. What is its value, in meters?Consider the following:A uniform magnetic field B= -0.033TK is present in a region of space, as shown in the figure. There is also a uniform electric field in this region of space. A protn with a constant velocity v = 74 m/s T passes through the region without deflection. What is the magnitude of the electric field in the region?