Atotal charge q is uniformly distributed on a ring of radius r in the xey plane centered on the origin. (a) calculate the electric field and potential at the center of the ring (b) consider a particle of mass m and charge -q constrained to slide along the z-axis. show that the charge will execute simple harmonic motion for small displacements about the origin and calculate the frequency of oscillation

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Current 1 of 8.4 a runs for 240 seconds and then stops. current 2 is 10.5 a. how long does current 2 have to un to deliver the same amount of charge as current 1? 88.28 192 s 2016 s 21,000 s

If steel is more dense that lake water, why can a boat float