How Is Current Calculated in a Mass Spectrometer?

[SHOORY]

Homework Statement

A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 multiplied by 10-25 kg and charge 3.20 multiplied by 10-19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1 m. After traveling through 180° and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup.

(a) What is the magnitude of the (perpendicular) magnetic field in the separator?

(b) If the machine is used to separate out 100 mg of material per hour, calculate the current of the desired ions in the machine.(c) In that case, calculate the thermal energy produced in the cup in 1.00 h.

Homework Equations

I=nqvA
Where I is the current
q is charge
v is the drift velocity
A is the cross-sectional area
and using energy equation we get that
v=(2Vq/m)^0.5
v is velocity
V is the potential difference

The Attempt at a Solution

I solved a and c but I couldn't solve b

 

[mfb]

How did you solve c without b?
Please show your solution for (c), from there it should be easy to find the answer to (b).

 

[SHOORY]

How did you solve c without b?
Please show your solution for (c), from there it should be easy to find the answer to (b).

thermal energy is equal to kinetic energy is equal to electric energy is equal to
potential difference * charge * number of charges
number of charges= whole mass in the cup after hour/ the mass of one particle

 

[mfb]

You have the number of charges and you have the time corresponding to it. Calculating the current should be straightforward.