A plane wave traveling through vacuum in the z direction encounters a perfect conductor occupying the region z ≥ 0, and reflects back: E(z, t) = E0 [cos(kz − ωt) − cos(kz + ωt)] ˆx, (z < 0). Requried:
a. Find the accompanying magnetic field (in the region z < 0).
b. Assuming B = 0 inside the conductor, find the current K on the surface z = 0, by invoking the appropriate boundary condition.
c. Find the magnetic force per unit area on the surface, and compare its time average with the expected radiation pressure.

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants

Madison lives near the ocean. she’s formed a hypothesis that increased concentrations of salt in the air speeds the corrosion of certain metals. if madison plans to test this hypothesis, she will have to deal with the following variables in her experiment: dependent variable: independent variable: one possible confounding variable:

Nthe 19th century, women were expected to conform to a certain role that entailed a. gaining domestic skills and establishing a career b. going to college and getting married c. getting married and having children d. graduating from college and being a housewife