Concept explainers
Review. Consider a capacitor with vacuum between its large, closely spaced, oppositely charged parallel plates. (a) Show that the force on one plate can be accounted for by thinking of the electric field between the plates as exerting a “negative pressure” equal to the energy density of the electric field. (b) Consider two infinite plane sheets carrying
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Physics for Scientists and Engineers
- An investigator has made a solenoid by wrapping 100 turns of wire on a tube that is 10 cm long and 2 cm in diameter. The power supply is providing as much current as it can, but a stronger field is needed, so the solenoid must be rewrapped. Which of the following will result in a stronger field?A. Wrapping 100 turns of wire on a tube that is 20 cm long and 2 cm in diameter.B. Wrapping 100 turns of wire on a tube that is 10 cm long and 1 cm in diameter.C. Wrapping 100 turns of wire on a tube that is 5 cm long and 2 cm in diameter.arrow_forwardIn situations where a small signal must travel over a distance,a shielded cable is used in which the signal wire is surrounded by an insulator and then enclosed by a cylindricalconductor (shield) carrying the return current. Why is a“shield” necessary?arrow_forwardAn electric current is flowing through a long cylindrical conductor with radius a = 0.75 m. The current density J = 9.5 A/m2 is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB. 1. For r = 0.5 a, calculate the numerical value of B in Tesla. 2. Express the magnitude of the magnetic field, B, at r > a in terms of I and r. 3. Express B in terms of J, a and r. 4. For r = 2 a, calculate the numerical value of B in Tesla.arrow_forward
- If the U-shaped conductor in the figure has resistivity ρ, whereas that of the moving rod is negligible, derive a formula for the current I as a function of time. Assume the rod starts at the bottom of the U at t=0 and moves with uniform speed v in the magnetic field B. The cross-sectional area of the rod and all parts of the U is A.arrow_forwardA conducting plate of thickness d carrying the current density of the field is placed in a region with an external magnetic field. Due to the influence of this conductor, the magnetic field in the chamber becomes separated by a magnitude of B₁ on the left side of the plate and B₂ on the other side. Determine the magnitude and direction of the plane current density carried by the plate for the two cases in the figure!arrow_forwardA portion of a long, cylindrical coaxial cable is shown in the figure below. An electrical current I = 3.0 amps flows down the center conductor, and this same current is returned in the outer conductor. Assume the current is distributed uniformly over the cross sections of the two parts of the cable. The values of the radii in the figure are r1 = 1.5 mm, r2 = 4.0 mm, and r3 = 7.0 mm. Using Ampere’s Law, find the magnitude of the magnetic field at the following distances from the center of the inner wire: a. 1.0 mm. b. 3.0 mm. c. 5.5 mm. d. 9.0 mm.arrow_forward
- A conducting rod of length ℓ moves on two horizontal, frictionless rails as shown inFigure P31.26. If a constant force of 1.00 N moves the bar at 2.00 m/s through amagnetic field B that is directed into the page (a) what is the current through the 8.00-Ω resistor R? (b) What is the rate at which energy is delivered to the resistor? (c) Whatis the mechanical power delivered by the force Fapp?arrow_forward. A solenoid has radius 5.80 mm, length 11.0 cm, 5000 turns, and is placed with its axis of symmetry along the x-axis, through the origin. A vector normal to the opening of the solenoid points to the right. We measure the resistance of the solenoid to be 14.0 Ω. The solenoid is in a region where the temperature is 49.0°C and initially, there is an external magnetic field of 0.30 T in the +x direction. Then the magnetic field is turned off and drops to 0 T over 50.0 milliseconds a. What is the magnitude of the average induced emf during the 50.0 milliseconds while the magnetic field magnitude decreases to 0? b. What is the direction of the induced current, as viewed from the right? Answer clockwise, counterclockwise, or zero and show work or explain in words. c. What is the magnitude of the induced current? d. What is the magnitude and direction of the induced magnetic field?arrow_forwardAt what velocity must a conductor 75 mm long cut a magnetic field of flux density 0.6T if an emf of 9V is to be induced in it? Assume the conductor, the field and direction of motion are mutually perpendicular.arrow_forward
- In a Hall-effect experiment, express the number density of charge carriers in terms of the Hall-effect electric field magnitude E, the current density magnitude J, and the magnetic field magnitude B.arrow_forwardAn airplane wingspan can be approximated as a conducting rod of length 30 m. As the airplane flies due north, it is flying at a rate of 78 m/s through the Earth's magnetic field, which has a magnitude of 46 µT toward the north in a direction 57° below the horizontal plane. What is the Hall emf (in V) along the wingspan?arrow_forwardConsider two protons trapped on the same geomagnetic field line. One proton has kinetic energy 10 eV and the other has kinetic energy of 10 keV. Which statement about the magnetic field strength at their respective mirror points is correct? A. B10 eV < B10 keV B. B10 eV > B10 keV C. B10 eV = B10 keV D. Not enough information is givenarrow_forward