Boundary conditions

(See attached file for full problem description with proper symbols and equations) --- If there is a field described by the vectors and . These are related by =k where k is a constant. The two vectors are found to satisfy the differential equations 1) =0 2) =0 questions: 1. Using these relations derive the boundary conditions that relate the values of the components of the vectors and on the two sides of a boundary between materials 1 and 2, where the constant k has two different values k and k in materials 1 and 2 respectively. 2. Now suppose that the boundary occupies the x-y plane (z=0). In medium 1 vector has components and =1. In medium 2, =2. Find the componen... click for more

Special relativity

1. This problem 12.25 from Griffiths’ book. The letters marking parts e and f have been cut off, but it should read: (e) Find proper velocity components… (f) As a consistency check verify…

Relativistic Collision

This is problem 12.34 from Griffiths’ third edition of Electrodynamics: In the past, most experiments in particle physics involved stationary targets: one particle (usually a proton or an electron) was accelerated to a high energy E, and collided with a target particle at rest (Fig12.29a). Far higher relative energies are obtainable (with the same accelerator) if you accelerate both particles to energy E, and fire them at each other. Classically, the energy E' of one particle, relative to other, is just 4E(why?)-not much of a gain (only a factor of 4). But relativistically the gain can be enormous. Assuming the two particles have the same mass m, show that E' = 2E^2/mc^2 - mc^2

Electrostatic Dipole

Coulomb’s law and electrostatic force. See attached files for full problem description.

Quadruple magnetic fields

(See attached file for full problem description)