What is the Magnetic Force on Arm Due to Sodium Ions in a Magnetic Field?

[balling12]

Homework Statement

Sodium ions (Na+) move at 0.844 m/s through a bloodstream in the arm of a person standing near a large magnet. The magnetic field has a strength of 0.259 T and makes an angle of 59.0° with the motion of the sodium ions. The arm contains 95.0 cm^3 of blood with a concentration of 2.50 X 10^20 Na+ ions per cubic centimeter. If no other ions were present in the arm, what would be the magnetic force on the arm?

Homework Equations

F=qvBsin(theta)

The Attempt at a Solution

F= q(.844m/s)(.259T)(sin59)
Thats as far as I have gotten. I am guessing that I need to use the volume of blood and concentration of ions to find the charge but I am not sure how to do so and have looked all through my textbook for help.

 

[kuruman]

The arm contains 95.0 cm^3 of blood with a concentration of 2.50 X 10^20 Na+ ions per cubic centimeter.

If there are 2.5x10²⁰ ions in 1 cm³, can you find how many ions are in 95 cm³?

If the force on one ion is (as you say) F= q(.844m/s)(.259T)(sin59), can you the total force on all the ions in the 95 cm³?

 

[balling12]

do i just multiply 95 by 2.5X10^20?

 

[kuruman]

What do you think?

 

[balling12]

well i tried that and once i worked it out the solution was wrong so I am guessing that was incorrect.

 

[kuruman]

Multiplying these two numbers is the correct thing to do. Whether you carried out the actual calculation correctly by pushing the right buttons on your calculator is another issue. If you show your calculation and the numbers you got, maybe someone will be able to figure out where you went wrong.

 

[balling12]

ok well i multplied the two numbers and got: 2.375X10^22. however once i plugged this into the equation to deteremine the magnetic force i got 4.45X10^21 which is incorrect so I am still unsure where i went wrong?

 

[noblegas]

Homework Statement

Sodium ions (Na+) move at 0.844 m/s through a bloodstream in the arm of a person standing near a large magnet. The magnetic field has a strength of 0.259 T and makes an angle of 59.0° with the motion of the sodium ions. The arm contains 95.0 cm^3 of blood with a concentration of 2.50 X 10^20 Na+ ions per cubic centimeter. If no other ions were present in the arm, what would be the magnetic force on the arm?

Homework Equations

F=qvBsin(theta)

The Attempt at a Solution

F= q(.844m/s)(.259T)(sin59)
Thats as far as I have gotten. I am guessing that I need to use the volume of blood and concentration of ions to find the charge but I am not sure how to do so and have looked all through my textbook for help.

dq=density*volume; That also helps

 

[kuruman]

ok well i multplied the two numbers and got: 2.375X10^22. however once i plugged this into the equation to deteremine the magnetic force i got 4.45X10^21 which is incorrect so I am still unsure where i went wrong?

You are not showing your calculation, just the result. Show how you multiplied, added, divided these numbers.

 

[balling12]

(95)(2.5X10^20)=2.375X10^22

(2.375X10^22)(.844)(.259)(sin59)= 4.4X10^21

 

[kuruman]

You need to redo your calculation. First off, the calculation as you show it above does not give 4.4x10²¹. Secondly, you did not include the charge on the ion.

 

[balling12]

well i re-did my calculation and every way i work it i still get that same answer. and i am not sure what you mean by calculating the charge on the ion.

 

[kuruman]

Look at the equation you posted:

F= q(.844m/s)(.259T)(sin59)

What does q stand for? Answer: The charge on the ion. Uncharged particles experience no force in a magnetic field whether they are moving or not.

 

[balling12]

So how do I find q?

 

[kuruman]

What is the charge on a singly ionized atom (Na⁺)?

 

[balling12]

im clueless

 

[kuruman]

Plenty of clues here.

http://en.wikipedia.org/wiki/Ion

 

[Bill Foster]

So how do I find q?

The total number of atoms/particles/whatever times the charge of each one.

The charge of an electron is http://lmgtfy.com/?q=charge+of+electron

A "singly ionized atom" means that a single electron has been lost. A sodium atom has 11 electrons. A singly ionized sodium atom has 10 electrons. Since it has 11 protons, it has a net charge of +e, where e is given by the charge of the electron in the link above.

 

[willem2]

So how do I find q?

q is in coulombs. How many Na+ ions are there in 1 coulomb?

 

[kuruman]

6.25x10¹⁸.

 

[balling12]

so what do i do with the 6.25X10^18?

 

[kuruman]

** Edit **

That's the answer to how many sodium ions in 1 coulomb. You can use that number or you can use what Bill Foster suggested in post #18

 

[balling12]

so do i need to multiply 1.6X10^-19 by 6.25X10^18 to get the charge(q)?

 

[kuruman]

A. 1.6x10^-19 Coulombs is the charge on one electron.

B. 2.375x10²² is the number Na⁺ ions you have in 95 cm³

C. q is the total charge on all the sodium atoms you have, it is measured in Coulombs.

D. Do what Bill Foster suggested.