Chapter 28, Problem 64P

GO Figure 28-52 gives the orientation energy U of a magnetic dipole in an external magnetic field $\stackrel{\to }{\text{B}}$, as a function of angle φ between the directions of $\stackrel{\to }{\text{B}}$ and the dipole moment. The vertical axis scale is set by U_s = 2.0 × 10^-4 J. The dipole can be rotated about an axle with negligible friction in order to change φ. Counterclockwise rotation from φ = 0 yields positive values of φ, and clockwise rotations yield negative values. The dipole is to be released at angle φ = 0 with a rotational kinetic energy of 6.7 × 10^-4 J, so that it rotates counterclockwise. To what maximum value of φ will it rotate? (In the language of Module 8-3, what value φ is the turning point in the potential well of Fig. 28-52?)

Figure 28-52 Problem 64.