77. A proton follows a spiral path through a gas in a uniform magnetic field of \( 0.010 \mathrm{~T} \), perpendicular to the plane of the spiral, as shown in Fig. 20-66. In two successive loops, at points \( P \) and \( Q \), the radii are \( 10.0 \mathrm{~mm} \) and \( 8.5 \mathrm{~mm} \), respectively. Calculate the change in the kinetic energy of the proton as it travels from \( \mathrm{P} \) to \( \mathrm{Q} \).
FIGURE 20-66
Problem 77.