Asquare loop of wire with sides of length l and carrying a conventional current i lies in the yz-plane with its center at the origin. a. what is the magnitude of the magnetic field due to this loop at a location x on the x-axis?
b. what is the approximate equation for the magnitude of the magnetic field at a location x that is much greater than l , in terms of the magnetic moment of the loop?
c. is the result of part (b) consistent with our previously derived result for the magnetic field of a magnetic dipole?
provide explaination.

Alarge box of mass m is pulled across a horizontal frictionless surface by a horizontal rope with tension t. a small box of mass m sits on top of the large box. the coefficients of static and

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)

What is the increase in density of a medium due to wave travel?