Equating mass and charge ratio of cathode rays

V)/(B^2r^2)In summary, The problem is to prove that q/m = (2V)/(B^2r^2) [2V over B-squared r-squared]. The individual provides a solution using various equations such as F[electric] = qE, F[magnetic] = Qvb, and F[centripital] = mv^2/r. They eventually reach the conclusion that q/m = (2V)/(B^2r^2) and ask for any insights on their method. They receive confirmation that their method is correct and the equation is proven.
  • #1
redruM
15
0
hi:smile:

i was approached by this problem,

prove q/m = (2V)/(B^2r^2) [2V over B-squared r-squared]

so far i have,

F[electric] = qE

F[magnetic] = Qvb

F[electric] = F[magnetic]

therefore, v = E/B

-----
now i am a bit confused/wrong
-----

E[kinetic] = (mv^2)/2

therefore, q x V = (mv^2)/2

therefore, q/m = E^2/(2VB^2)

jus by looking at the result, i have to get E= 2V/r.

any insights will be greatly appreciated...
if my method even correct?
 
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  • #2
F[magnetic] = qvB

Elecrons will be deflected in a circular path, so

F[centripital] = mv^2/r

Equate these, and get v = Bqr/m

Electrons accelerate through a potential, so

E[kinetic] = mv^2/2 = qV

Substitute v = Bqr/m into this, and solve for q/m.
 
  • #3
thanks a lot..

works out perfectly
 

1. What are cathode rays?

Cathode rays are streams of electrons that are produced when an electric current is passed through a gas.

2. How did scientists determine the mass and charge ratio of cathode rays?

Scientists used a device called a cathode ray tube, which allowed them to observe the behavior of cathode rays and measure their properties.

3. What is the significance of equating the mass and charge ratio of cathode rays?

This experiment helped to confirm the existence of electrons and their properties, providing evidence for the existence of subatomic particles.

4. How does the mass and charge ratio of cathode rays relate to atomic structure?

The discovery of the mass and charge ratio of cathode rays helped to support the idea that atoms are made up of smaller, indivisible particles with negative charges (electrons).

5. Are cathode rays still studied today?

While cathode ray tubes are no longer in common use, the properties and behavior of cathode rays are still studied and applied in fields such as particle physics and electron microscopy.

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