Electrical Properties of a Dielectric Cylinder
To determine the electric properties of the dielectric cylinder, we need to consider the volume charge density and the distance from the axis of the cylinder. The given volume charge density is 10⁻⁵C/m³.
a) Electric Charge per Unit Length:
The electric charge per unit length of the cylinder can be calculated using the formula λ = ρπa², where ρ is the charge density and a is the radius of the cylinder.
b) Electric Induction, Electric Field Intensity, and Polarization Vectors at 10 cm:
At a distance of 10 cm from the axis of the cylinder, the electric induction is D = ελ/(2πR), where ε is the vacuum permittivity and R is the distance.
c) Electric Induction, Electric Field Intensity, and Polarization Vectors at 1 cm:
Similarly, the electric properties at a distance of 1 cm from the axis can be calculated using the same formulas as in part b.
d) Electric Potential of the Cylinder:
The electric potential of the cylinder can be determined by integrating the electric field intensity equation over the surface of the cylinder.
For part a, the electric charge per unit length λ = ρπa². For part b, the electric induction at 10 cm is given by D = ελ/(2πR), while for part c, the properties at 1 cm can be calculated using the same formulas. Finally, part d involves finding the electric potential by integrating the electric field intensity equation.