Velocity of colliding electron and surface

AI Thread Summary
An insulating sphere with a radius of 5.00 mm carries a total charge of 4.25 x 10^-12 Coulombs, and an electron starts from rest at a distance of 9.00 mm from its surface. The problem involves calculating the electron's velocity upon collision with the sphere by applying conservation of energy principles. Initial and final potential energies (PEi and PEf) are determined using the formula PE = (k*q1*q2)/r. The correct approach requires subtracting the initial potential energy from the final potential energy and equating it to half the mass times the velocity squared, leading to the expected result of 1.31 x 10^6 m/s for the electron's speed at impact. Properly applying the equations and ensuring the correct order of subtraction is crucial for achieving the correct answer.
sheepcountme
Messages
80
Reaction score
1

Homework Statement



An insulating sphere has a radius of 5.00 mm and has a total charge of 4.25 x 10-12 Coulombs, distributed uniformly over its surface. And electron starts from rest at a distance of 9.00mm from the surface and accelerates towards it. How fast in the electron moving when it crashes into the sphere's surface?


Homework Equations



PEe=(kq1q2)/r

W=deltaPEe

V(electric potential around point charge)=(kq)/r

The Attempt at a Solution



I'm afraid I just don't know where to begin. I've been playing around with these equations but I can't get a velocity to fall out.
 
Physics news on Phys.org
What is the initial PE and KE of the electron?

What is the final PE and KE of the electron?

Apply the conservation of energy equation and find the final velocity of the electron.
 
Okay, so using PEi+KEi=PEf+KEf...

k, and the charges are constant (I got 6.13x10^21 for the numerators of the PEf and PEi).
Dividing this by the changes in distance I got 1.233x10^-18 at 5mm for PEf and 6.81x10^-19 at 9mm for PEi. Since the electron is starting from rest, I get..

PEi-PEf=.5mv^2

subtracting PEf from PE i I got -1.23 and divided by the mass of an electron (9.12x10^-31) however this will leave me taking the square root of a negative number to get the velocity so I must be doing something wrong.

Also the book says our answer should be 1.31x10^6
 
When the electron is at 9mm, the PE of the system PEi = k*q*e/(9*10^-3)

When the electron is at 5mm, the PE of the system PEf = k*q*e/(5*10^-3)

Now PEf - PEi = 1/2*m*v^2.

Substitute the values and find v.
 
Ah, okay, I was subtracting final from initial. Thank you!
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Gauss' law and Faraday cage problem
Replies
10
Views
2K
Why Is Work Positive When Done Against the Electric Field?
Replies
22
Views
3K
Find the equation of this magnetic field
Replies
6
Views
1K
Calculating the number of electrons given the force of repulsion
Replies
5
Views
4K
Potential at center of sphere of radius R and charge -Q
Replies
14
Views
2K
Electric Flux through Cubical Surface Enclosing Sphere
Replies
2
Views
4K
Electric field sphere calculations with a hollow cavity using Gauss' law
Replies
21
Views
4K
Calculating voltage within and outside of a solid sphere
Replies
1
Views
2K
Calculating the surface charge of a sphere and a conducting shell
Replies
5
Views
4K
Finding Escape Speed for an Electron that's Initially at Res
Replies
9
Views
6K

Hot Threads

Recent Insights

Back
Top