A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of 0.25 A. The relative permeability of the core is 80. (a) What is the magnetic field in the core?
(b) What part of the magnetic field is due to atomic currents?

Acar accelerates from 5.0 m/s to to 11 m/s at a rate of 3.0 m/s^2. how far does it travel while accelerating? 20m 117m 43m 16m

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.

Arigid tank is divided into two equal parts by a partition. one part of the tank contains 3 kg of compressed liquid water at 400 kpa and 60°c while the other part is evacuated. the partition is now removed, and the water expands to fill the entire tank. determine the entropy change of water during this process, if the final pressure in the tank is 40 kpa. use steam tables.