A 0.50-m long solenoid consists of 1000 turns of copper wire wound with a 4.0 cm radius. When the current in the solenoid is 18 A, the magnetic field at a point 1.0 cm from the central axis of the solenoid is

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.

Aforklift raises a 1,020 n crate 3.50 m up to a shelf. how much work is done by the forklift on the crate? the forklift does j of work on the crate.

Two point charges are on the y axis. a 3.90-µc charge is located at y = 1.25 cm, and a -2.4-µc charge is located at y = −1.80 cm. (a) find the total electric potential at the origin. v (b) find the total electric potential at the point whose coordinates are (1.50 cm, 0). v