A uniform magnetic field exists in a circular area. A particle carrying charge \(q=5.0 \mathrm{mC}\) is placed in the field a distance \(r_{\mathrm{p}}=20 \mathrm{~mm}\) from the center of the circular area. If the particle experiences a force that has magnitude \(F=4.00 \mu \mathrm{N}\) and is perpendicular to the direction of the magnetic field, at what rate is the magnetic field changing?