An electron is relased into a uniform electric field of magnitude 8.35 N/C. How many times larger is this electrons acceleration than the acceleration due to gravity on the surface of Earth?
Is it just F= qE = ma (for the electron, and using E for electric field), and then take the a as a ratio of g? It seemed too simple, I'm afraid I'm missing a variable.
set qE=mg*k
solve for k
Hi, I tried this question...should we use g as -9.8m/s^2?
You're on the right track! To find the acceleration of the electron in the electric field and compare it to the acceleration due to gravity on Earth's surface, you can use the equation F = qE = ma.
Here's how you can approach the problem step-by-step:
1. Determine the force acting on the electron due to the electric field: F = qE.
- "q" represents the charge of the electron, which is constant and equal to 1.6 x 10^-19 C.
- "E" is the magnitude of the electric field, given as 8.35 N/C.
Therefore, the electric force (Fe) on the electron is Fe = (1.6 x 10^-19 C)(8.35 N/C).
2. Use Newton's second law to find the acceleration (a) of the electron: Fe = ma.
- Rearrange the equation to solve for acceleration: a = Fe/m, where "m" is the mass of the electron.
- The mass of an electron is very small and can be approximated as 9.1 x 10^-31 kg.
Substitute the values into the equation to find the acceleration of the electron (ae).
3. Calculate the acceleration due to gravity (ag) on the surface of Earth.
- The acceleration due to gravity, ag, is approximately 9.8 m/s^2.
4. Finally, compare the acceleration of the electron (ae) to the acceleration due to gravity (ag).
- Take the ratio of ae to ag to determine how many times larger the electron's acceleration is compared to gravity.
To summarize, the steps are:
1. Calculate the electric force (Fe) on the electron.
2. Use Newton's second law to find the acceleration (ae) of the electron.
3. Calculate the acceleration due to gravity (ag) on the surface of Earth.
4. Compare the acceleration of the electron (ae) to the acceleration due to gravity (ag).
Let me know if you need help with any specific calculations or if you have further questions!