The work done by an external force on an electron as it moves from point A to point B is 6.3 × 10-14 J. If it was started from rest and had 3 × 10-14 J of kinetic energy when it reached B, what is the potential difference VB-VA?
To find the potential difference between point B and point A, we need to use the conservation of energy.
The work done by an external force on an object is equal to the change in its kinetic energy. In this case, the work done on the electron is 6.3 × 10^(-14) J, and its kinetic energy at point B is 3 × 10^(-14) J.
We can set up the equation as follows:
Work done = Change in kinetic energy
6.3 × 10^(-14) J = (3 × 10^(-14) J) - 0 (since the electron started from rest)
Now, let's solve for the potential difference (VB-VA).
We know that the change in kinetic energy is equal to the change in potential energy, which is given by the potential difference multiplied by the charge of the electron (e).
Change in kinetic energy = Change in potential energy
(3 × 10^(-14) J) - 0 = e(VB-VA)
The charge of an electron (e) is approximately 1.6 × 10^(-19) C. Substituting this value into the equation, we have:
(3 × 10^(-14) J) - 0 = (1.6 × 10^(-19) C)(VB-VA)
Now solve for VB-VA:
(3 × 10^(-14) J) = (1.6 × 10^(-19) C)(VB-VA)
Dividing both sides by (1.6 × 10^(-19) C):
(3 × 10^(-14) J) / (1.6 × 10^(-19) C) = VB-VA
Using a calculator, we can calculate the potential difference (VB-VA):
VB-VA ≈ 1.875 × 10^5 volts
Therefore, the potential difference between point B and point A is approximately 1.875 × 10^5 volts.