A silver wire has resistivity p = 1.60 × 10-8 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 Units (b) Number i Units (c) Number i Units
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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 -DetectorThree long parallel wires, lie perpendicular to this page, as shown in the figure, and carry the same current intensity I = 2 A. The current along the wire A is going into the page. The current along the wire B is also going into the page. The current along the wire C is coming out of the page. Knowing that d = 1 cm, find the direction and magnitude of the net force per unit length acting on the wire B. (Force per unit length just means divide the force by the length.) 2d d A ВSuppose that the current density carried by an infinite cylindrical wire is not uniform but in fact varies as Jz(u) = J0 * [1 - (u2 / R2)], where J0 is the value of the current density at the wire's center, R is the radius of the wire, and u is distance from the axis of the wire. Assuming that the magnetic field is circular, compute the wire's magnetic field both inside and outside the wire. (Ampere's law makes even nonuniform current densities manageable.) (Hint: The answer is BФ = 0.25 * μ0 * J0 * R on surface at u = R.)
- 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 35.6-meter-long spacecraft flies past a neutron star, and passes through the neutron star s extremely powerful magnetic field of strength 7.95 x 10^4 T. The spacecraft travels at a velocity of 2.43 km/s in a direction perpendicular to the magnetic field; the spacecraft s long axis is also perpendicular to the magnetic field. What is the induced emf (voltage) between the two ends of the spacecraft? 6.88E+08 V 6.88E+09 V 6.88E+06 V 6.88E+05 VA 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
- Given: 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.An 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.