What Potential Difference Is Needed to Stop an Electron?

[eprparadox]

Homework Statement

What potential difference is needed to stop an electron having an initial speed of 4.2*10^5 m/s?

Homework Equations

W = delta K
W = q*delta V

The Attempt at a Solution

So I'm pretty sure that the potential difference should be negative in order to stop the electron, but I keep getting a positive answer (the correct magnitude, but incorrect sign).

I set delta K = q*delta V.

I know delta K will be less than zero since K(final) < K(initial) and q should also be negative since we're dealing with an electron. But this gives me a positive delta V.

Where am I going wrong?

Thanks in advance.

 

[rock.freak667]

so you have 1/2 mv²=VQ

for an electron Q=-1.60*10^-19C

 

[tomcue]

I would first confirm that my assumption about the potential difference being negative to stop an electron is correct. To do this, I would refer to the fundamental equation for potential difference: delta V = W/q, where W is the work done on the electron and q is its charge. Since the question does not provide any information about the work done on the electron, I would assume it to be zero. In that case, the potential difference would also be zero, meaning that no potential difference is needed to stop the electron. This makes sense intuitively as well, since the electron has an initial speed and no external force is acting on it, it would eventually come to a stop on its own without any potential difference.

If the question is indeed asking for the minimum potential difference required to stop the electron, then we need to consider the work done on the electron. In this case, we can use the equation W = delta K to calculate the work done, where delta K is the change in kinetic energy of the electron. Since the electron is being brought to a stop, its final kinetic energy would be zero. Therefore, the work done on the electron would be equal to its initial kinetic energy. Plugging this into the equation for potential difference, we get delta V = K(initial)/q. Since the electron has a negative charge, q will also be negative, resulting in a negative potential difference. This confirms our initial assumption that the potential difference needed to stop the electron should be negative.

The issue with getting a positive answer could be due to a calculation error. I would recommend double-checking the units and making sure that all the values are correctly plugged into the equations. It could also be helpful to draw a diagram or use a graph to visualize the problem and understand the direction of the potential difference. Finally, I would suggest practicing more problems to strengthen the understanding of the concept.