The formula for finding v(z) given volume charge density is v(z) = ∫ρ(z) dz, where ρ(z) is the volume charge density and ∫ is the integral of the function over the given range.
The volume charge density can be determined by dividing the total charge of the system by its volume. This can be written as ρ = Q/V, where Q is the total charge and V is the volume of the system.
Yes, v(z) can be negative or zero. This depends on the distribution of the volume charge density and the range of the integral. If the volume charge density is negative over the given range, the value of v(z) will also be negative.
The value of v(z) will change depending on the range of the integral. If the range is increased, the value of v(z) will also increase, and vice versa. This is because a larger range means a larger volume of charge is being integrated, resulting in a higher value for v(z).
Yes, the unit for volume charge density is coulombs per cubic meter (C/m^3). This unit is derived from the SI unit for charge (coulombs) and the SI unit for volume (cubic meters).