The electric flux through a certain area of a dielectric is (8.76 × 10³ V.m/sª)tª. The displacement current through that area is 12.9 pA at time 26.1 ms. Calculate the electric permittivity (dielectric constant) E.
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- 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 UnitsA 0.220–A current is charging a capacitor that has circular plates 10.1 cm in radius. The plate separation is 4.00 mm. (a) What is the time rate of increase of electric field between the plates? V/(m·s)(b) What is the magnetic field between the plates 5.00 cm from the center? T
- A large water main is 2.25 m in diameter and the average water velocity is 6.75 m/s. If there are some slight impurities in the water, it can easily become a conductor and this flow represents a small electrical current. d = 2.25 mv = 6.75 m/s Find the Hall voltage produced if the pipe runs perpendicular to the Earth’s 5.00 × 10-5 T field.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·m2Given: B = 5 * 10-5 T ẑ; σ = 4 (Ohm-meters)-1 (conductivity) a) Assume that seawater is moving at a constant velocity v = v0 ŷ and that the Earth’s magnetic field is along the ẑ-direction. Calculate the electric current density J produced by the magnetic force. Hint: first compute the force per unit charge, F/q, and then use the relationship J = σ(F/q). b) Derive the equation of motion of a cylindrical differential volume element of base area δA and height δh parallelto the direction of J. Assume that seawater has a known volumetric mass density ρ. Show that this equation implies that the velocity satisfies the following differential equation:dvy/dt = vy/τwhere τ is a constant that you should write in terms of B, σ, and ρ.
- 005 A uniform electric field of magnitude 5.06 x 10 V/m throughout a cylindrical volume re- sults in a total energy of 2.95 µJ. What magnetic field over this same region stores the same total energy? Answer in units of T.A 48 turn coil of wire creates a circular area of 6.95 cm2. If a magnetic field of 90.79 T hits this area at a right angle, what is the magnetic flux (in Wb) through the coil?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.