What is the escape speed of an electron launched from the surface of a 1.5 cm diameter glass sphere that has been charged to 10 nC?
Which equation(s) would I use?
I have tried and I did not find anything.
I guess more people are asking the same question right now, because early, there was nothing.
To calculate the escape speed of an electron launched from the surface of a charged glass sphere, we need to use the following equations:
1. Coulomb's Law: F = k * |q1 * q2| / r^2
This equation determines the electric force between two point charges, q1 and q2, at a distance r apart. Here, k is the electrostatic constant (8.99 x 10^9 N m^2/C^2).
2. Electric Potential Energy: U = k * |q1 * q2| / r
This equation represents the potential energy between two point charges, q1 and q2, separated by a distance r.
3. Kinetic Energy: KE = (1/2) * m * v^2
This equation calculates the kinetic energy of an object with mass m and velocity v.
The escape speed of an electron refers to the minimum speed needed for the electron to overcome the electric potential energy barrier and escape from the sphere's influence. Hence, we need to find the kinetic energy required to overcome the potential energy barrier.
To calculate the escape speed, we can equate the kinetic energy to the potential energy:
(1/2) * m * v_escape^2 = k * |q * q_electron| / r
In this equation, m represents the mass of the electron, q is the charge of the sphere, q_electron is the charge of an electron, and r is the radius of the sphere (which is half of the diameter). We can rearrange the equation to solve for v_escape:
v_escape = √((2 * k * |q * q_electron|) / (m * r))
Now we have the equation needed to calculate the escape speed of the electron.
try google first
I saw several discussions of problems just like yours.
You must not have tried too hard, because I got several hits, such as
https://answers.yahoo.com/question/index?qid=20070429182156AAn5Pem
which is the exact same problem, but with different numbers.