physics help please

[waffles8000]

soo i have this huge booklet of questions due on thursday and all of them are really hard

there was one in particular i needed help with so i googled it

and i found the exact question

 

but i need help with the solution cuz i have no idea how to prove it

i found it on this site, http://www.chegg.com/homework-help/questions-and-answers/figure-shows-essentials-mass-spectrometer-used-measure-masses-ions-ion-mass-m-charge-q-pro-q9983543

but i need a subscription to look at the solution

 

can someone help me pls

[Guardian of the Galaxy]

The particle starts off with kinetic energy equal to the charge times the voltage drop

 

E = q * V

 

Kinetic energy = 1/2 m * v^2 so

 

E = 1/2 m * v^2 

 

q * V = 1/2 m * v^2

 

m = 2qV/v^2

 

The moving charge will experience a Lorentz force in B, where F = q*(v x B), where the magnitude is q*(magnitude of v) * B and the direction is perpendicular to v.

 

|F| = q|v|B

 

Also the formula for uniform circular motion tells us that the force required to maintain circular motion is F = mv^2/r, where r is the radius of rotation. Here, r = X/2

 

F = q*v*B = 2*mv^2/X

 

=> v = qBX/2m

 

Substituting v into the first equation...

 

m = 2qV/(qBX/2m)^2

 

m = (2qV * 4m^2 )/(q^2 * B^2 * X^2)

 

B^2 * X^2 * q/(8V) = m

 

As desired.

 

(B and v are vector quantities of course but I just use them to denote their magnitudes here, no need to deal with vector equations since B is perpendicular to v)

[waffles8000]

The particle starts off with kinetic energy equal to the charge times the voltage drop

 

E = q * V

 

Kinetic energy = 1/2 m * v^2 so

 

E = 1/2 m * v^2 

 

q * V = 1/2 m * v^2

 

m = 2qV/v^2

 

The moving charge will experience a Lorentz force in B, where F = q*(v x B), where the magnitude is q*(magnitude of v) * B and the direction is perpendicular to v.

 

|F| = q|v|B

 

Also the formula for uniform circular motion tells us that the force required to maintain circular motion is F = mv^2/r, where r is the radius of rotation. Here, r = X/2

 

F = q*v*B = 2*mv^2/X

 

=> v = qBX/2m

 

Substituting v into the first equation...

 

m = 2qV/(qBX/2m)^2

 

m = (2qV * 4m^2 )/(q^2 * B^2 * X^2)

 

B^2 * X^2 * q/(8V) = m

 

As desired.

 

(B and v are vector quantities of course but I just use them to denote their magnitudes here, no need to deal with vector equations since B is perpendicular to v)

thank you so soo much!!! you are a genius TT