A point charge q with mass m is released from rest at the origin in an external magnetic field and an external electric field. Both external fields are uniform (constant in magnitude and direction). The electric field is in the z direction and the magnetic field is in the x direction: E= Eoz, B= Box

where Eo and Bo are constants. The electric field will accelerate the point charge. Once the point charge has acquired a non-zero velocity it will experience a magnetic force as well. Using Newton's second law and the Lorentz force law, show that the motion of the point charge must obey the following equations:

d^2x/dt^2= 0, d^2y/dt^2= ωdz/dt, d^2z/dt^2= ω(Eo/Bo- dy/dt)

where ω is the cyclotron frequency.

ω= qBo/m

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w