# Homework Help: Electric potential and velocity

1. May 21, 2013

### san203

Hello all. I had written a test today on ELECTRIC POTENTIAL and I got this particular question wrong:

1. The problem statement, all variables and given/known data

If an electron would travel from a region of low potential to a region of high potential , would there be a change in velocity?

2. My take at the problem : electric potential is a location based quantity which is nothing but just P.E. /charge.
So if an electron were to go from low potential to higher potential , then it would increase its potential energy. the work done by electric field(assuming their is a electric field) would be negative in magnitude and hence decrease the velocity

The answer : velocity does not change
How is this possible?

Last edited: May 21, 2013
2. May 21, 2013

### ehild

You correctly stated that the the electric potential is equal to the potential energy of a charged body divided by the charge. The charge of the electron is negative: so at higher potential its potential energy is more negative than at low potential. When the electron goes from law potential to high one, its potential energy decreases. The electric field is conservative, so what happens to the kinetic energy of the electron?

That is certainly not true.

ehild

3. May 22, 2013

### san203

I see. So by conservation of energy, the velocity of particle should increase.
Am I right in saying that the answer you gave was based on the assumption that the field was created by a negative charge?
Because the question does not state anything about the type of field.

My teacher's answer : As their is no field , their should be no force and hence no change in velocity.

So how could their be a electric potential when their is no field?

4. May 22, 2013

### ehild

There is field if the potential changes. If there is electric field, there is force on a charged particle. If there is force when a particle travels through a distance, there is work. If work is done, the KE of the particle changes.

ehild

5. May 24, 2013

### anhnha

ehild,
Let say the electron moves from A to B with VA < VB
The potential energy of the electron at A and B:
WA = q*VA
WB = q*VB
Where q = -1.6*10^-19C
If 0<VA<VB => WA > WB
=> When electron moves from A to B its potential enery decreases => its kinetic energy increases and its velocity increases
Is this right?

How about the case VA < 0 < VB?
Then WB < 0< WA => KE (at B) < KE (at A) => its velocity decreases.
Is this also right?

6. May 24, 2013

### ehild

It is right.

No. It is the same as before. If VA<VB, the sign of the potential does not matter.

Let be VA=-10 V and VB = 5 V
As the charge of the electron is negative, qVA>qVB: WA=1.6x10-19*10 J, WB=-1.6x10-19*5. You see that WA>WB. As energy is conserved, KE(A)+WA=KE(B)+WB --->WA-WB=KE(B)-KE(A) >0 KE(B)>KE(A), the KE energy increases, the speed also increases.

ehild

7. May 24, 2013

### anhnha

Get it now, thanks ehild

8. May 24, 2013

### ehild

You are welcome

ehild