Acoil 4.20 cm radius, containing 470 turns, is placed in a uniform magnetic field that varies with time according to b=( 1.20×10 −2 t/s )t+(2.55×10 −5 t/s4 )t4. the coil is connected to a 580-ω resistor, and its plane is perpendicular to the magnetic field. you can ignore the resistance of the coil.
a)
find the magnitude of the induced emf in the coil as a function of time.
b)
what is the current in the resistor at time t0 = 4.50 s ?

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 ?

Could someone . i have tried to solve myself but my calculation is off

If we relied solely on the nonrenewable resources found in the u.s., which one would we run out of first at current usage levels? a. natural gas b. oil c. uranium d. coal