3. a rectangular coil of wire (a = 21.0 cm, b = 45.0 cm) containing a single turn is placed in a uniform 7.80 t magnetic field, as the drawing shows. the current in the loop is 18.0 a. determine the magnitude of the magnetic force on the right side 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.

Where is the potential energy throughout the loading, cocking, and releasing of the trebuchet?

What are the north and south poles of a solenoid change with?