A current-carrying, rectangular coil of wire is placed in a magnetic field. The magnitude of the torque on the coil is not dependent upon which one of the following quantities? a. the magnitude of the current in the loop
b. the area of the loop
c. the direction of the current in the loop
d. the orientation of the loop
e. the length of the sides of the loop

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

The energy of a photon was found to be 3.38 × 10–19 j. planck’s constant is 6.63 × 10–34 j • s. which color of light corresponds to this photon?

Could we see a galaxy that is 20 billion light-years away?