Q1. Assume a finite thin linear antenna with length l is positioned along the z-axis symmetrically. The current distribution is described as follows Iz (z') = 10(2+1). (10(2-12). ≤ z < 0, 0 ≤z'≤ a) Find the Vector Potential A in the Far-Field Region. (Explain each step!) b) Compute the spherical E and B fields in the Far-Field Region. (Explain each step!) (Hint: (1) Use far-field approximation in radial distances. (2) After finding A₂ component, use A₁ = âe (sin 0 Az), A4 = 0 to transform into spherical forms. (3) Then, use curl in spherical coordinates for part b).)

I Review I Constants During most of its lifetime, a star maintains an equilibrium size in which the inward force of gravity on each atom is balanced by an outward pressure force due to the heat of the nuclear reactions in the core. But after all the hydrogen "fuel" is consumed by nuclear fusion, the pressure force drops and the star undergoes a gravitational collapse until it becomes a neutron star. In a neutron star, the electrons and protons of the atoms are squeezed together by gravity until they fuse into neutrons. Neutron stars spin very rapidly and emit intense pulses of radio and light waves, one pulse per rotation. These "pulsing stars" were discovered in the 1960s and are called pulsars. Part A = 2.0 x 1030 kg) and size (R 3.5 x 10° m) of our sun rotates once every 35.0 days. After undergoing gravitational collapse, A star with the mass (M the star forms a pulsar that is observed by astronomers to emit radio pulses every 0.100 s. By treating the neutron star as a solid sphere,…

A

Consider a model of an electron as a hollow sphere with radius R and the electron charge -e spread uniformly over that surface. d. Use Einstein’s equation relating rest mass to energy to derive a value for R. Unfortunately, your answer will be model-dependent. The traditional “Classical radius of the electron” is derived by setting the electrostatic work to be e2/(4pi e0 R)

High-Energy Cancer Treatment. Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 1012 W) pulses of light that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell without causing it to explode, as long pulses would do. We can model a typical such cell as a disk in 3 mm diameter, with the pulse lasting for 7 ns with an average power of 7.4 x10¹2 W. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. How much energy is given to the cell during this pulse? (answer in 2 decimal places and in MegaJoule (MJ)) m, = 4px 107T. m/ A c = 3 x 108 m/s e 8.85 x 10-¹2 C²/Nm²

5. (Physics) The mass of a region D with density function 8(x, y) is given by | 5(x, y)dA. Suppose a circular metal disk of radius 3 lies in the ry-plane with its center at the origin. At a 1 distance r from the origin, the density of the metal per unit area is ổ = Find the total mass r2 +1 of the disk.

Questão 5 Quantum tunneling was applied in 1928 by physicist George Gamow (and others) to explain the alpha emission of nuclear radiation, as we will see in the topic of nuclear physics. The alpha particle, whose mass is m = 6.64 x 10^(-27) kg, remains attached to the nucleus due to a strong interaction with the other nuclear constituents (nucleons) which overcomes the electrostatic repulsion between them, resulting in a graph of potential energy shown in figure A, where R is the range of the strong force and is of the order of the nuclear radius. However, note that there may be states for the alpha particle with energy E > 0 that can “tunnel” the Coulomb potential barrier. Consider a one-dimensional approximation for the potential energy well of an alpha particle in a 15 fm wide Uranium core (equivalent to the core diameter), in which the Coulomb barrier was modeled as a 20 fm wide rectangular barrier and 30 MeV high (see figure B). Knowing that the longest de Broglie wavelength…

laplace and poisson equation Assume that V is a function of y and at y =2, V=5 volt and at y = 4, V = 10 volt. a) Find V, E, E and draw these with respect to y-axis. b) Now if p₂ = 30μc m³ and E, 3. Find V, E, E and draw these with respect to y-axis. Q2:

An proton is confined within a region of width 3.22 x 10-¹1 m. What is the minimum kinetic energy of a proton? A. 41.66 J. B. 1.70 x 10¹6 J. C. 8.02 x 10-22 J. D. 6.99 x 10-50 J.