# For what time does an electron move after current turned off?

Tags:
1. Nov 22, 2014

### bananabandana

Hi,
Can someone point me in the right direction in terms of calculating the length of time an electron in a wire would continue to move after the current is turned off?
Can we use the drift velocity in some way?
Thanks!

2. Nov 22, 2014

### nsaspook

The electron movement is the current in the wire so I'm not sure what you mean "after the current is turned off".

3. Nov 22, 2014

### Simon Bridge

You want the impulse or step responce for the circuit.... For the DC case, where you are opening a switch from a voltage source at t=0, the signal is v(t)=V(1-u(t)).

This will tell you how the current dies down.

On the scale of individual electrons, they never stop moving.

4. Nov 22, 2014

### sophiecentaur

Current is zero: drift velocity is zero.
There is no (real) circuit in which the current can stop instantly (a step); the transition from current to no current will always take time and there will be a waveform - perhaps a slow change or it may involve 'ringing' as the current goes to zero. Simon Bridge's post says that, in a more formal way.

5. Nov 22, 2014

### bananabandana

Thanks. What are [tex] u(t) [\tex] and [tex] v(t) [\tex] please?

6. Nov 22, 2014

### Simon Bridge

V and I are voltages and currents that do not vary with time.
v and i are voltages and currents that do vary with time.

v(t) just says "voltage as a function of time".
u(t) is the unit (or Heaviside) step function.

So $v(t)=Vu(t)$ just says that the voltage was switched on at time t=0, and $v(t)=V\big(1-u(t)\big)$ says that the voltage V was switched off at time t=0

7. Nov 23, 2014

### ZapperZ

Staff Emeritus

First of all, if one pays attention to the original post, there's something not quite right with the way the question is being asked. As nsaspook has stated, "current" is the net movement of electrons. So if the current is "turned off", then there's no net movement! That's like asking "how fast am I moving if my speed is zero?" Did the OP meant potential difference?

Secondly, at first glance, one would want to answer this in a simplistic, elementary picture. But then, the concept of "drift velocity" is brought in. And from my perspective, I start to question if the OP understands the statistical nature of the electron gas in metals (remember, the question is about electron movement in a wire!). If so, then the simplistic, elementary picture isn't sufficient, because at a finite temperature, electrons simply don't stop moving, and so the answer to the question of when electrons stop moving after the potential difference is zero is NEVER.

When the question is vague and faulty, and the scenario and level of the question is unknown, then the question becomes a bigger puzzle than the actual physics being asked.

Zz.

8. Nov 24, 2014

### nasu

Maybe a rough estimate would be the relaxation time (τ) used in free electron gas models. (like Drude's model)
In metals the electrons "loose" their drift component due to thermal motion in a time of the order of 10^(-15) s.