10 Figure 29-33 shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of f B ds taken in the directions shown, most positive first.
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Figure 29-33 shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of f B ds taken in the directions shown, most positive first.
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- Wire 2 *34 O Figure 29-62 shows, in cross section, two long straight wires held against a plastic cylinder of ra- dius 20.0 cm. Wire 1 carries current 4 = 60.0 mA out of the page and is fixed in place at the left side of the cylinder. Wire 2 carries current i, = 40.0 mA out of the page and can be moved around the cylinder. At what (positive) angle 6, should wire 2 be positioned such that, at the origin, the net magnetic field due to the two currents has magnitude 80.0 nT? Wire 1- %3D Figure 29-62 Problem 34.longitudinally-uniform, and axially-symmetric 2. The current distribution of an infinite, wire can be described in cylindrical coordinates by J = J(p)ź. (a) Show that · ƒ = 0. (b) Considerations of longitudinal and axial symmetry require that the mag- netic field can only depend upon p, i.e. that = Ẻ(p) = B₂(p)ô+ Bø(p)❖ + B₂(p)ź. Use Ampère's Law to determine Bo(p) in terms of I(p) = 2π ff J(p') p'dp'. (c) Use the Biot and Savart Law to show that Bp(p) = B₂ (p) = 0. Side note: it is pretty easy to show that Bp(p) must be zero using Gauss's Law for B with a cylindrical volume. I am not aware of an "easy" way to see B(p) 0 not that it is very difficult using the Biot and Savart Law... (d) Use the integral form for the vector potential [Jackson, Eq. (5.32)] to determine A for this current distribution. Hint: in order to deal with divergent integrals, you may want to limit the current distribution to -L≤ zThe figure shows two closed paths wrapped around two conducting loops carrying currents i₁ = 6.9 A and i₂ = 4.1 A. What is the value of the integral B ds for (a) path 1 and (b) path 2? (a) Number i (b) Number i Units Units(a) The figure below shows two parallel conducting rails 15.2 cm apart, connected by a resistor with resistance R₂ = 5.00 Q. Two metal rods with resistances R₁ = 11.40 and R₂ = 15.0 (2 slide along the rails with negligible friction. Rod R₁ slides to the left at constant speed v₁ = 4.00 m/s, while rod R₂ slides at speed v₂ = 2.00 m/s. The rods and rails are in the presence of a uniform magnetic field pointing into the page, perpendicular to the plane of the rails, with a magnitude of Bin = 0.0100 T. +5 x x x x x x x x x x x x x x x x x x x x x x x x x x upward x x x ---Select--- X * x x x x x x x x Rg x x x x x R₁ R₂ What are the magnitude (in μA) and direction of the current through resistor R₂? μA magnitude direction x x x x (b) What If? What are the magnitude (in μA) and direction of the current through resistor R. if the rods move inward, instead of outward, with the same speeds as in part (a)? μA magnitude directionFor a solenoid in vacuum of length l = 10 cm with 104 turns per meter calculate the current required to create the field B= 70 μT. Provide your answer in SI units.The above picture depicts a moveable vertical conducting bar sliding on fixed conducting rails. v → = 2.3 m/s and B → is 0.65 T and out of the page. What is the current in the system? Group of answer choices 0.30 A 1.5 A 0.012 A 0 A 7.5 AA cylindric mica insulator to be used between a 100 kV DC line and ground has a diameter of 5 cm. The insulator is expected to prevent currents of more than 1 nA^1 . Find the minimum required length of the porcelain cylinder.(5) Current is flowing through a cylindrical copper wire with radius 6.33mm and length 92.1cm. This wire is hooked up to two capacitors in series C1 The capacitors both have cross sectional areas of A = 179cm2. (a) At a given moment in time, the current is I electrons is vd = 9.42µF and C2 = 8.11µF. = 77.97A and the drift velocity of the 45.6µm/s. What is the number density of electrons in this wire? (b) At a given moment in time, the charge on capacitor 2 is 62.6µC. What is the total change in potential across both capacitors combined? | (c) At the moment described in part (b), what is the energy stored in capacitor 2? (d) At the moment described in part (b), what is the energy density of the electric field in capacitor 2? :