A proton moves through a region containing a uniform electric field given by E = 32.0 ĵ V/m and a uniform magnetic field B = (0.200 î + 0.300 ĵ + 0.400 k) T. Determine the acceleration of the proton when it has a velocity v = 230 î m/s.

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)

Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular aluminum plates, each 11 cm in diameter, separated by 1.0 cm. how much charge can be added to each of the plates before a spark jumps between the two plates? for such flat electrodes, assume that value of 3×106n/c of the field causes a spark.

Consider an ideal gas at 27.0 degrees celsius and 1.00 atmosphere pressure. imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube. what is the length l of an edge of each small cube if adjacent cubes touch but don't overlap?