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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鈥檚 molten outer core. If the radius of their circular path is 3500 km, calculate the current they produce.
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Figure 28-28 shows the path of an electron in a region of uniform magnetic field. The path consists oftwo straight sections, each between a pair of uniformly charged plates, and two half-circles. Which plate isat the higher electric potential in
(a) the top pair of plates and
(b) the bottom pair?
(c) What is the direction of the magnetic field?
Prove that the relation holds not only for the rectangular loop of Figure but also for a closed loop of any shape. (Hint:Replace the loop of arbitrary shape with an assembly of adjacent long, thin, approximately rectangular loops that are nearly equivalent to the loop of arbitrary shape as far as the distribution of current is concerned.)
In Figure 28-40, an electron with an initial kinetic energy ofkeV enters region 1 at time t= 0. That region contains a uniform magnetic field directed into the page, with magnitude . The electron goes through a half-circle and then exits region 1, headed toward region 2 across a gap ofcm. There is an electric potential difference 鈭�V across the gap, with a polarity such that the electron鈥檚 speed increases uniformly as it traverses the gap. Region 2 contains a uniform magnetic field directed out of the page, with magnitude T. The electron goes through a half-circle and then leaves region 2. Atwhat time tdoes it leave?
Figure 28-52 gives the orientation energy Uof a magnetic dipole in an external magnetic field , as a function of angle between the directions , of and the dipole moment. The vertical axis scale is set by . The dipole can be rotated about an axle with negligible friction in order that to change . Counterclockwise rotation from yields positive values of , and clockwise rotations yield negative values. The dipole is to be released at angle with a rotational kinetic energy of , so that it rotates counterclockwise. To what maximum value of will it rotate? (What valueis the turning point in the potential well of Fig 28-52?)
A conducting rectangular solid of dimensions dx= 5.00 m, dy= 3.00 m, and dz=2.00 m moves at constant velocity through a uniform magnetic field (Fig. 28-35)What are the resulting (a) electric field within the solid, in unit-vector notation, and (b) potential difference across the solid?
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