Question

The drift velocity of electrons in a conductor connected to a battery is given by v_d = `(−"eE" τ)/"m"`. Here, e is the charge of the electron, E is the electric field, τ is the average time between collisions and m is the mass of the electron.

Based on this, answer the following:

1. How does the drift velocity change with a change in the potential difference across the conductor?
2. A copper wire of length 'l' is connected to a source. If the copper wire is replaced by another copper wire of the same area of cross-section but of length '4l', how will the drift velocity change? Explain your answer.

Answer 1

1. As the potential difference across the conductor is increased, the electric field set-up inside the conductor increases. Since v_d ∝ E, drift velocity also increases with an increase in potential difference.
2. Given v_d ∝ E
   but E = `"V"/"l"`
   ∴ `"v"_"d" ∝ (1/"l")`
   As length increases to 4l, drift velocity becomes `(1/4)`th of the original value.