Find the magnitude of the current density

[Sho Kano]

Homework Statement

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?

Homework Equations

J = nev

n = electron density
e = electron charge
v = drift velocity

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?

 

[gneill]

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

 

[Sho Kano]

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

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

 

[Sho Kano]

OH WAIT,
n = [cm^-3]

 

[Sho Kano]

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

n = 3.95e14 m^-3?

 

[gneill]

How many cubic centimeters in a cubic meter?

 

[Sho Kano]

How many cubic centimeters in a cubic meter?

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

 

[gneill]

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

 

[Sho Kano]

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

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

 

[gneill]

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

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

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

 

[Sho Kano]

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

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

 

[gneill]

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.