Volumetric Current Density in Moving Cylinder
What is the formula for calculating the volumetric current density in a short wooden cylinder with non-uniformly distributed charge?
Formula for Volumetric Current Density
How can the volumetric current density be calculated when the cylinder moves parallel to its axis with uniform acceleration?
Calculation of Volumetric Current Density in Parallel Motion
Part (a): When the cylinder moves parallel to the axis with uniform acceleration a, the current flows due to the motion of charges inside the cylinder. The force acting on the charges is given by F = ma. The current I can be expressed as I = neAv, where n is the number density of charges, e is the charge of each charge carrier, A is the cross-sectional area of the cylinder, and v is the velocity of the charges. The charge Q is non-uniformly distributed in the volume, but squared with the length, so the charge density is given by ρ = Q/L³. The number density of charges is n = ρ/N, where N is Avogadro's number. The volumetric current density J can be expressed as: J = I/V = (I/L²)R = (Q/RL³)e(N/L³)a. The volumetric current density J is independent of the acceleration a, so it remains constant throughout the motion of the cylinder.How can the volumetric current density be calculated when the cylinder rotates around the axis with uniform angular acceleration?