A silver wire has resistivityp = 1.20 x 10-8 2-m and a cross-sectional area of 5.30 mm2. The current in the wire is uniform and changing at the rate of 2350 A/s when the current is 140 A. (a) What is the magnitude of the (uniform) electric field in the wire when the current in the wire is 140 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 distancer from the wire?
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- Three 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.
- There is a 8 m wire with a current of 15 amps exposed horizontally between two concrete walls. What is the magnitude of the B-field in micro-tesla (u T) 1 m up from the wire and 3.8 m out from the left wall?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.
- A length of copper wire carries a current of 11 A, uniformly distributed through its cross section. Calculate the energy density of (a) the magnetic field and (b) the electric field at the surface of the wire. The wire diameter is 2.3 mm, and its resistance per unit length is 4.5 2/km. (a) Number 1.456 Units J/m^3 (b) Number 0.0000000000000175 Units J/m^3A circular conducting loop with a radius of 1.00 m and a small gap filled with a 10.0 resistor is oriented in the xy-pane. If a magnetic field of 2.0 T, making an angle of 30° with the z-axis increases to 9.0 T, in 2.0 s, what is the magnitude of the current that will be caused to flow in the conductor?Answer referring to example 26.7
- Consider the cylindrical conductor with a hollow center and copper walls of thickness b-a as shown. The radii of the inner and outer walls are a and b respectively. and the current I is uniformly spread over the cross section of the copper (shaded region). What is the magnitude of the magnetic field in units of nT at r- 24.1cm. a=13cm, b=30.5cm, 7- 200mA, Hom4 x 10 Tm/A. Provide your answer with two decimal places. A -- 01 (out of page)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.What is the displacement current density? a) The current density due to the motion of charges in a conductor. b) The current density due to the motion of charges in a dielectric. c) The current density that arises from time-varying electric fields in free space. d) The current density that arises from the magnetic fields produced by moving charges. In what form can Ampere-Maxwell's equation be written in the absence of a time-varying electric field? a) V. E = p/ɛo b) VxE=-ƏB/ət c) V x H = J d) VB=0 What does the integral form of Ampere-Maxwell's equation relate to? a) The electric field generated by a time-varying magnetic field. b) The magnetic field generated by a time-varying electric field. c) The relationship between the current density and the magnetic field. d) The behavior of electromagnetic waves in free space. e) None In the integral form of Ampere-Maxwell's equation, what does the surface integral of the displacement current density represent? a) The total charge enclosed by…