# Electric Current

## Problems from IIT JEE

**Problem (IIT JEE 1997):**
A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is (are),

- current, electric field and drift speed
- drift speed only
- current and drift speed
- current only

**Solution: **
In steady state, charge can not accumulate in a conductor. Thus, constant current $i={\mathrm{d}q}/{\mathrm{d}t}$ flows along the length of conductor. The current density at a point having cross-section area $A$ is given by $J={i}/{A}$. The current density is related to electric field by $J=\sigma E$, where conductivity $\sigma$ is a material property. The drift velocity $v_d$ is given by $i=neAv_d$. Thus, both $E$ and $v_d$ are inversely proportional to $A$.