A uniform magnetic field exists in a circular area. A particle carrying charge \(q=3.0 \mu \mathrm{C}\) is placed in the field a distance \(r_{\mathrm{p}}=5 \mathrm{~cm}\) from the center of the circular area. If the magnetic field drops at a constant rate of \(0.2 \mathrm{~T} / \mathrm{s}\), what its the magnitude and direction that an external force should have so that the particle remains fixed in its position? \(\cdot\)

The next four problems are based on the situation illustrated in Figure P29.40. A uniform magnetic field pointing in the positive \(\mathrm{z}\) direction fills a cylindrical volume of space of radius \(\mathrm{R}\) whose central axis is the \(\mathrm{z}\) axis. Outside this region, there is no magnetic field.

Figure P29.40