The instantaneous B(x. y, z; t) in vacuum is given by B = a,B, cos(2y) sin(w – nz) + a,B, cos(2x) cos(w – nz) Determine the electric displacement current density assuming that there is no source current at point x and y.
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- 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 -DetectorA silver wire has resistivity p = 1.60 × 108 Q-m and a cross-sectional area of 2.20 mm2. The current in the wire is uniform and changing at the rate of 2850 A/s when the current is 180 A. (a) What is the magnitude of the (uniform) electric field in the wire when the current in the wire is 180 A? (b) What is the displacement current in the wire at that time? (c) What is the ratio of the magnitude of the magnetic field due to the displacement current to that due to the current at a distance r from the wire? (a) Number i Units (b) Number i Units (c) Number i Units
- A magnetic field of strength 0.29 T is directed perpendicular to a plane circular loop of wire of radius 29 cm. Find the magnetic flux through the area enclosed by this loop.A (8.42x10^-1)-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 (2.047x10^0) nA through a cross section of the region? Provide your answer in V/(m.s) with three significant figures.A magnetic field of strength 0.25 T is directed perpendicular to a plane circular loop of wire of radius 23 cm. Find the magnetic flux through the area enclosed by this loop. T·m2
- The figure shows a circular region of radius R = 2.50 cm in which a uniform electric flux is directed out of the plane of the page. The total electric flux through the region is given by PE = (3.00 mV-m/s)t, where t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a)1.50 cm and (b)7.50 cm? (a) Number i (b) Number i eTextbook and Media Units Units RAn infinite length line carries current I in the +az direction on the z-axis, and this is surrounded by an infinite length cylindrical shell (centered about the z-axis) of radius a carrying the return current I in the -az direction as a surface current. Find expressions for the magnetic field intensity everywhere. If the current is 1.0 A and the radius a is 2.0 cm, plot the magnitude of H versus radial distance from the z-axis from 0.1 cm to 4 cm.Figure CQ19.7 shows a coaxial cable carrying current I in itsinner conductor and a return current of the same magnitudein the opposite direction in the outer conductor. Themagnetic field strength at r = r0 is B0. Find the ratio B /B0 at(a) r = 2r0 and (b) r = 4r0.