The following table gives the length of three copper wires, their diameters, and the applied potential difference across their ends. Arrange the wires in increasing order according to the following:

(a) The magnitude of the electric field within them,

(b) The drift speed of electrons through them, and

(c) The current density within them.

a) We know that electric field of a line charge E =

where λ = charge per unit length = q/L

We know that potential difference V = W/q

Therefore

Therefore E₂ < E₃ < E_1.

b) Drift velocity

Drift velocity is inversely proportional to the area

Area (A) = πd²/4

Current

We know that potential difference V = W/q

n = q/e

Therefore

Therefore V_d2< V_d3 < V_d1

c) Current density J = I/A

I =nAeV_d

J = σE

J = n e V_d

Therefore J₂< J₃< J₁