# Find the magnitude of the current density

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1. Apr 3, 2016

### Sho Kano

1. The problem statement, all variables and given/known data
A beam contains 3.95×108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.64×105 m/s. What is the magnitude of the current density?

2. Relevant equations
J = nev

n = electron density
e = electron charge
v = drift velocity
3. The attempt at a solution
J = nev
J = 3.95e8 * 1.6e-19 * 2 * 1.64e5
J = 2.07e-5 A/m^2

I'm getting marked wrong for this?

2. Apr 3, 2016

### Staff: Mentor

Check the units of all the factors to make sure you're not mixing different measures.

3. Apr 3, 2016

### Sho Kano

It works out,
n = [m^-3]
e = [C]
v = [m/s]
n*e*v = C/s*m^2 = A/m^2

4. Apr 3, 2016

OH WAIT,
n = [cm^-3]

5. Apr 3, 2016

### Sho Kano

n = 3.95e14 m^-3?

6. Apr 3, 2016

### Staff: Mentor

How many cubic centimeters in a cubic meter?

7. Apr 3, 2016

### Sho Kano

$3.95e8\frac { 1 }{ cm\^ 3 } *\frac { 100cm }{ m } *\frac { 100cm }{ m } *\frac { 100cm }{ m }$

8. Apr 3, 2016

### Staff: Mentor

So then, what's the charge density in coulombs per cubic meter?

9. Apr 3, 2016

### Sho Kano

2*1.6e-19 / 3.95e14 m^-3 = 8.101e-34

8.101e-34 * 1.63e5 = 1.32e-28 ?

10. Apr 3, 2016

### Staff: Mentor

No. Why did you divide by the number density? That makes the m^-3 into m^3 in the numerator.

11. Apr 3, 2016

### Sho Kano

Yea my bad, I'm just not into it today. So it's,
3.2e-19 * 3.95e14 = 1.26e-4

1.26e-4*1.64e5 = 20.72

12. Apr 3, 2016

### Staff: Mentor

That's better.

You need to add units to your result. Also, you should avoid rounding intermediate values during calculations as that introduces rounding and truncation errors that can creep into your significant figures. Only round at the end for presentation of results.