Question

A potential difference V is applied across a conductor of length l and cross-sectional area A. Briefly explain how the current density J in the conductor will be affected if

1. the potential difference V is doubled.
2. the conductor was gradually stretched to reduce its cross-sectional area to `A/2` and then the same potential difference V is applied across it.

Answer 1

1. If potential difference 'V' is applied across a conductor of length 'l' and area of cross-section 'A' having the number of free electrons per unit volume n.
   Then, the charge in the conductor,
   q = neAl
   and I = `q/t`
   I = neAυ_d and υ_d = `(eE)/m xx tau`
   where τ is the relaxation time and 'm' is the mass of the electron.
   Therefore, the current per unit area i.e., current density,
   J = `I/A`
   J = neυ_d
   J = `n e xx (eE)/m xx tau`
   J = `(n e^2tau)/m xx (V/l)`
   Hence, with an increase in potential different V, J increases.
2. J does not change when the area decreases because, according to relation (i), J is not reliant on A.