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A closed curve encircles several conductors. The line integral
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- In a long, .straight, vertical lightning stroke, electrons move downward and positive ions move upward and constitute a current of magnitude 20.0 kA. At a location 50.0 m east of the middle of the stroke, a free electron drifts through the air toward the west with a speed of 300 m/s. (a) Make a sketch showing the various vectors involved. Ignore the effect of the Earth's magnetic field. (b) Find the vector force the lightning stroke exerts on the electron. (c) Find the radius of the electrons path. (d) Is it a good approximation to model the electron as moving in a uniform field? Explain your answer. (e) If it does not collide with any obstacles, how many revolutions will the electron complete during the 60.0-s duration of the lightning stroke?arrow_forwardFigure 22.30 (Quick Quiz 22.6) Four closed paths around three current-carrying wires. Rank the magnitudes of Bds for the closed paths a through d in Figure 22.30, from greatest to least.arrow_forwardReview. The use of superconductors has been proposed for power transmission lines. A single coaxial cable (Fig. P23.73) could carry a power of 1.00 103 MW (the output of a large power plant) at 200 kV, DC, over a distance of 1.00 103 km without loss. An inner wire of radius a = 2.00 cm, made from the superconductor Nb3Sn, carries the current I in one direction. A surrounding superconducting cylinder of radius b = 5.00 cm would carry the return current I. In such a system, what is the magnetic field (a) at the surface of the inner conductor and (b) at the inner surface of the outer conductor? (c) How much energy would be stored in the magnetic field in the space between the conductors in a 1.00 103 km superconducting line? (d) What is the pressure exerted on the outer conductor due to the current in the inner conductor? Figure. P23.73arrow_forward
- Hall potentials are much larger for poor conductors than for good conductors. Why?arrow_forwardThe wire carrying 440 A to the motor of a commuter train feels an attractive force per unit length of 4.60 10-3 N/m due to a parallel wire carrying 5.00 A to a headlight. (a) How far apart are the wires? m(b) Are the currents in the same direction? Yes or Noarrow_forwardTwo long, parallel wires, each having a mass per unit length of 25.0 g /m, are supported in a horizontal plane by strings l = 5.00 cm long. When both wires carry the same current I, the wires repel each other so that the angle ? between the supporting strings is 10.0 °. Find the magnitude of the current. (Your result must be in units of Amperes. Include 1 digit after the decimal point and maximum of 4% of error is accepted in your answer.Take gravitational acceleration g = 9.81 m /s 2, vacuum permeability µ 0 = 4π x 10 -7 T /A 2 and π = 3.14.)arrow_forward
- A long straight wire in the z-axis carries a current of 6.0 A in the positive z direction, and a circular loop of 10 cm radius in the xy-plane also carries 1.0-A current as shown in the figure. Point P in the center of the ring is 25 cm from the z-axis. An electron is ejected from P at a velocity of 1.0 × 106 m / s in the negative x direction. What is the y component of the force acting on the electron? (e = 1.60 × 10-19 C, μ0 = 4π × 10-7 T m / A)arrow_forwardTwo very long, parallel wires are separated by d = 0.065 m. The first wire carries a current of I1 = 0.75 A. The second wire carries a current of I2 = 0.65 A. Express the magnitude of the force between the wires per unit length, f, in terms of I1, I2, and d.arrow_forwardTwo parallel wires separated by 2.00 cm attract to each otherwith a force per unit length of 3.00 · 10−4 N/m. The current in one wireis 4.00 A. (a) Find the current in the other wire. (b) Are the currents inthe same direction or in opposite directions? (c) What would happen ifthe direction of one current were reversed and doubled?arrow_forward
- In a particular region there is a uniform current density of 15 A/m2 in the positive z direction. What is the value of when that line integral is calculated along a closed path consisting of the three straight-line segments from (x, y, z) coordinates (4d, 0, 0) to (4d, 3d, 0) to (0, 0, 0) to (4d, 0, 0), where d = 20 cm?arrow_forwardConsider two current-carrying wires, separated by a distance d = 4.9 cm, as shown in the figure. The left wire is directed out of the page with current I1, and the right wire is directed into the page with current I2. The point P is a distance d from both wires, so the wires and the point form an equilateral triangle. If the current from the first wire is 7.5 A and the current from the second is 15 A, what is the magnitude of the magnetic field, in tesla, at point P?arrow_forwardTwo long wires hang vertically. Wire 1 carries an upward current of 1.50 A. Wire 2, 20.0 cm to the right of wire 1, carries a downward current of 4.00 A. A third wire, wire 3, is to be hung vertically and located such that when it carries a certain current, each wire experiences no net force. (a) Is this situation possible? Is it possible in more than one way? Describe (b) the position of wire 3 and (c) the magnitude and direction of the current in wire 3.arrow_forward
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