a. A steady current flows in a metallic conductor of non - uniform cross section. State which of the quantities i.e., current density, electric field, and drift velocity, current density, electric field, and drift velcoity remain constant?
b. A steady current passes through a cylindrical conductor. Is there an electorn field inside the conductor?

Explanation

a. As by definition, current and current density are related tyo
each other through J = I//S, so for steady current
(i.e., I = constant) but nonuniform cross sectin J will not
be constant but will vary cross - sectional area S.
`As J prop (I)/(S)`
Now, as J is related to electric field E and drift velocity`v_d`
through the relations `J = sigmaE and J = "ne"v_d`
`E =(I)/(sigmaS) and v_d = (I)/("ne"S) [as J = (I)/(S)]`
But as sfor a given metal `sigma` and n are constants, so
`E prop(1)/(S) and v_d prop(I)/(S) [as I = "constant"]`
i.e., in case of steady current flow through a meatllic
conductor of nonuniform corss section, currrent is constant
while current density, electric field, and drift velcoity are not
constant and all very inversely with area fo cross section.
b. Yes, current flows in a conductor only when electric field
established within the conductor exerts force on the electrons.