A uniform electric field of magnitude 410 N/C pointing in the positive x-direction acts on an electron, which is initially at rest. The electron has moved 3.00 cm.
(a) What is the work done by the field on the electron?(b) What is the change in potential energy associated with the electron?(c) What is the velocity of the electron?
I need help with C. I have the work as 1.97e-18, b is -1.97e-18. and for C I am using the square root of the answer for v = 2/m(w). My answer is 4.85e-23. I need it to be converted to m/s. I have no idea how but the answer is supposed to be something like 1.9e+06
Your numbers are not useful or correct without the dimensions that go with them.
When an electron moves 0.03 m under the influence of a 410 N/C E-field, work is done on it equal to
410 N/C*1.6*10^-19C*0.03m = 1.968*10^18 J
That becomes its kinetic energy.
So your (a) and (b) are correct.
V = sqrt(2E/m), where m is the mass of the electron and E is the kinetic energy.
The mass of an electron is 9.11* 10^-31 kg
Awesome! Thanks it worked out, I had the mass of an electron wrong. That was my problem there.
To find the velocity of the electron (part c), you can use the equation that relates work and kinetic energy. The work done by the electric field on an electron is equal to the change in its kinetic energy.
(a) Work Done by the Electric Field:
You mentioned that you have already calculated the work done by the electric field as 1.97e-18 J. This is the correct value.
(b) Change in Potential Energy:
According to the conservation of energy, the change in potential energy of the electron is equal to the negative of the work done by the electric field. You correctly found this to be -1.97e-18 J.
(c) Finding the Velocity of the Electron:
To find the velocity of the electron, you can use the equation that relates work to kinetic energy:
Work = 1/2 * m * v^2,
where m is the mass of the electron and v is its velocity.
To find the mass of an electron, we can use its known mass, which is approximately 9.1e-31 kg.
Rearrange the equation to solve for v:
v^2 = (2 * Work) / m,
v = sqrt((2 * Work) / m).
Substituting the known values:
v = sqrt((2 * 1.97e-18 J) / 9.1e-31 kg).
To convert the answer to m/s, you can use scientific notation. The answer 4.85e-23 m/s is in scientific notation. To convert it to a more common form:
4.85e-23 m/s = 4.85 * 10^(-23) m/s.
Alternatively, you can convert the scientific notation to standard decimal notation by multiplying the number by the appropriate power of 10:
4.85 * 10^(-23) = 0.0000000000000000000000485 m/s.
Therefore, the value of the velocity of the electron is approximately 0.0000000000000000000000485 m/s or 4.85e-23 m/s.
It seems that the answer you mentioned, around 1.9e+06 m/s, does not match the calculations. Please double-check your calculations or reevaluate if there might be a mistake in the formula or input values used.