Find the de Broglie wavelength λλlambda for an electron moving at a speed of 1.00×106m/s1.00×106m/s. (Note that this speed is low enough that the classical momentum formula p=mvp=mv is still valid.) Recall that the mass of an electron is me=9.11×10−31kgme=9.11×10−31kg, and Planck's constant is h=6.626×10−34J⋅sh=6.626×10−34J⋅s.

Aspring with a mass of 2 kg has a damping constant 14 kg/s. a force of 3.6 n is required to keep the spring stretched 0.3 m beyond its natural length. the spring is stretched 0.6 m beyond its natural length and then released. find the position of the mass at any time t. (assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)

The most important difference between a wedge and an inclined plane is a. their size b. their shape c. how they are used d. what they are made of

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.