A particle with charge q is at the origin and is given an initial velocity

A particle with charge q is at the origin and is given an initial velocity v=vox. The magnetic field in the origin is b=boz and the electric field is E=Eoy. Determine the path of the particle (that is, find its position as a function of time, and interpret the results). Begin by showing that the path lies in a single plane. Determine the center and radius of any circles. Do not make assumptions about the value of vo. Please check the attachment which contains the appropriate notation. Thanks! :)

Using Divergence (Gauss) and Curl (Stokes) theorems

(See attached file for full problem description with proper equations and symbols) --- 1. In the year 2075 physicists discover a new field described by the vectors and . These are related by = k Where k is constant. The two vectors are found to satisfy the differential equations * = 0 (* means dot) And x = 0 a. 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 k1 and k2 in materials 1 and 2 respectively. b. Now suppose that the boundary occupies the x-y plane (z=0). In the medium 1 vector... click for more

An infinite cylinder

(See attached file for full problem description) --- 2. An infinite cylinder of radius a, with dielectric constant 0 has its axis along the z-axis. There is a uniform electric field 0 a large distance from the cylinder. (a) Find the electric field everywhere inside and outside the cylinder. (b) Find the bound charge density on the surface of the cylinder (c) Draw a field line diagram showing the electric field everywhere. (An explanation is good enough)

Magnetic field at the centre of a rotating uniformly charged hemispherical shell.

3. A uniformly charged hemispherical shell is rotating with angular speed w (omega) about its symmetry axis as shown. Use the Biot-Savart Law to find the magnetic field at the center of the sphere (point P). Begin by discussing the direction of B. See attached file for full problem description.

Magnetic fields

(See attached file for full problem description) 4. A particle with charge q is at the origin and is given an initial velocity = v0 . The magnetic field in the region is = B0 and the electric field is = E0 . Determine the path of the particle (that is, find its position as a function of time, and interpret the results). Begin by showing that the path lies in a single plane. Determine the center and radius of any circles. Do not make any assumptions about the value of v0.