A recently developed method to study brain function is to produce arapidly changing magnetic field within the brain. When thistechnique, known as TMS, is applied to the prefrontal cortex, forexample, it can reduce a person's ability to conjugate verbs, though other though processes are unaffected. The rapidly varyingmagnetic field is produced with a circular coil of 21 turns and aradius of 6.0 cm placed directly on the head. The current in thisloop increases at the rate of 1.2x107A/s (by discharginga capacitor. (a) At what rate does the magnetic field at the centerof the coil increase? (b) Suppose a second coil with half the areaof the first coil is used instead. Would your answer to part (a)increase, decrease, or stay the same? By what factor?