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Chapter 28: Q58P (page 832)
The magnetic dipole moment of Earth has magnitude . Assume that this is produced by charges flowing in Earth’s molten outer core. If the radius of their circular path is 3500 km, calculate the current they produce.
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Question: Figure 28-56 shows a homopolar generator, which has a solid conducting disk as rotor and which is rotated by a motor (not shown). Conducting brushes connect this emf device to a circuit through which the device drives current. The device can produce a greater emf than wire loop rotors because they can spin at a much higher angular speed without rupturing. The disk has radius and rotation frequency , and the device is in a uniform magnetic field of magnitude that is perpendicular to the disk. As the disk is rotated, conduction electrons along the conducting path (dashed line) are forced to move through the magnetic field. (a) For the indicated rotation, is the magnetic force on those electrons up or down in the figure? (b) Is the magnitude of that force greater at the rim or near the center of the disk? (c)What is the work per unit charge done by that force in moving charge along the radial line, between the rim and the center? (d)What, then, is the emf of the device? (e) If the current is , what is the power at which electrical energy is being produced?
Bainbridge’s mass spectrometer, shown in Fig. 28-54, separates ions having the same velocity. The ions, after entering through slits, S1and S2, pass through a velocity selector composed of an electric field produced by the charged plates Pand P', and a magnetic field perpendicular to the electric field and the ion path. The ions that then pass undeviated through the crossedand fields enter into a region where a second magnetic field exists, where they are made to follow circular paths. A photographic plate (or a modern detector) registers their arrival. Show that, for the ions, q/m=E/rBB,where ris the radius of the circular orbit.
A wire lying along a yaxis from y=0to y=0.250mcarries a current of 2.00mAin the negative direction of the axis. The wire fully lies in a nonuniform magnetic field that is given by
In unit-vector notation, what is the magnetic force on the wire?
A circular coil of 160 turns has a radius of 1.92cm. (a)Calculate the current that results in a magnetic dipole moment of magnitude 2.30 Am2 . (b)Find the maximum magnitude of the torque that the coil, carrying this current, can experience in a uniform 35.0 mTmagnetic field.
A particle of charge q moves in a circle of radius r with speed v. Treating the circular path as a current loop with an average current, find the maximum torque exerted on the loop by a uniform field of magnitude B.
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