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Chapter 29: Q. 11 (page 829)
The south pole of a bar magnet is brought toward the current loop of FIGURE Q29.11. Does the bar magnet attract, repel, or have no effect on the loop? Explain.
The magnet will repel the loop.
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Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring. Consider a proton ring with 36 identical bending magnets connected by straight segments. The protons move along a -m-long circular arc as they pass through each magnet. What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of ? Assume that the field is uniform inside the magnet, zero outside.
a. An infinitely long sheet of charge of width L lies in the x y plane between x=-L / 2 and x=L / 2. The surface charge density is \eta. Derive an expression for the electric field at height above the centerline of the sheet.
b. Verify that your expression has the expected behavior if and if
c. Draw a graph of field strength E versus z.
A spherically symmetric charge distribution produces the electric field E u = 15000r2 2nr N/C, where r is in m.
a. What is the electric field strength at r = 20 cm?
b. What is the electric flux through a 40-cm-diameter spherical surface that is concentric with the charge distribution?
c. How much charge is inside this 40-cm-diameter spherical surface?
A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is . At this field strength, the Hall voltage on the probe iswhen the current through the probe is. Later, when an unknown magnetic field is measured, the Hall voltage at the same current is. What is the strength of this magnetic field?
The magnetic field strength at the north pole of a - diameter, -long Alnico magnet is . To produce the same field with a solenoid of the same size, carrying a current of , how many turns of wire would you need?
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