Along, thin solenoid has 390 turns per meter and a radius of 1.20 cm. the current in the solenoid is increasing at a uniform rate didt. the magnitude of the induced electric field at a point which is near the center of the solenoid and a distance of 3.48 cm from its axis is 8.00×10−6 v/m.
calculate di/dt.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

The experiment done in lab is repeated, using a ball that has unknown mass m. you plot your data in the form of f 2 versus m/l, with f in rev/s, m in kg, and l in m. your data falls close to a straight line that has slope 3.19 m/(kg · s2). use g = 9.80 m/s2 and calculate the mass m of the ball.

Since the energy was not raising the temperature of the water during these segments, what was the energy used to do instead? your answer must include an explanation of what is happening to the molecules.