Finding an impedance of conducting medium

Could you please assist with the problem attached? Thank you.

the motion of a particle in uniform electric and magnetic fields

Full question is attached. 1) In this question we will consider the motion of a charged particle in uniform electric and magnetic fields that are perpendicular. You may ignore the effects of gravity throughout this question. a) i) Consider a charged particle of mass m and charge q which is moving in a uniform electric field E = Eey and a perpendicular uniform magnetic field B = Bez. Show that the equations of motion for the particle are, ii) If the particle is at rest at time t = 0, verify that iii) Hence determine the position of the particle at time t, assuming that it was located at the origin at t = 0 b) An infinite metal plate occupies the xz-plane (y=0). The plate is kept... click for more

Inductance, energy and amplitude of induced current on an inductor consisting of 500 turns.

An inductor consists of 500 turns of wire of resistance 6.0 Ω wound tightly and uniformly on a toroidal ring of an insulating magnetic material with relative permeability μ = 40. The material is linear so μ is independent of the magnetic field. The mean radius of the toroid is 15 cm and the cross sectional area is 1.0 cm2. (there are 4 parts to this question (fulll quesion in attachment, the first is) a) Starting from Ampere’s law, calculate the self inductance of the coil, assuming that the cross sectional area of the coil is sufficiently small that we can assume that the magnetic field has constant strength inside the coil. Please can you fully show your working to... click for more

Use the integral version of Gauss's law to find the electric field and the electric displacement in a cylindrical capacitor.

A capacitor consists of two concentric long cylindrical conductors of radii a and c, where c > a, and each is of negligible thickness. The space between the conductors is filled with two layers of dielectric materials. Using cylindrical co-ordinates with z-axis along the axis of the cylindrical conductors, the space aclick for more

Force on moving charge, charge density free electron density.

The full question is attached and comes in two parts, the first requires me to find the magnetic force acting on a point charge the second asks me to determine the charge density and current density of the current electrons in the wire as well as the residual positive charge in the wire? Please help and show you working.