Curent densitys relation to drift velocity

In summary, the beam contains 4.0x10^8 doubly charged positive ions per cubic centimeter, all moving north with a speed of 1.2x10^5 m/s. To calculate the total current in the ion beam, the magnitude and direction of the current density must be known, which can be calculated using the formula J=I/A=nqv. The ion density must be converted to particles per cubic meter, as the current density must be in C/m2.
  • #1
DODGEVIPER13
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Homework Statement


A beam contains 4.0x10^8 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.2x10^5 m/s.

(a) What is the magnitude of the current density ?
(b) What is its direction?
(c) What additional quantity or quantities are needed to calculate the total current in this ion beam?

Homework Equations


J=I/A=nqv (v = drift velocity)


The Attempt at a Solution


Well I tried this (4.0e8)(2)(1.6e-19)(1.2e5) which I thought would give what I wanted but apparently not. I was thinking by looking a dimensional analysis that it has something to do with the seconds in the velocity but I am not sure?
 
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  • #2
Take care with the units of length. The ion density is given in particles/cubic centimeters, the velocity is given in m/s. The current density has to be in C/m2.

ehild
 
  • #3
Ok I did that I converted (4e8) in particles/ cubic centimeter to 400 particles per cubic meter but it still did not give the right answer?
 
  • #4
There are 400000000 particles in one cm3. How many cm3 makes one m3? (which one is bigger? 1 cm3 or 1 m3?) Where are there more particles? In a big volume or in the small volume?

ehild
 
  • #5
Huh wait your confusing me I though 400 cubic meters was correct is it not?
 
  • #6
What was 400 cubic meters?

ehild
 
  • #7
im saying the conversion from cubic centimeters to cubic meters is 400
 
  • #8
I got it thanks for all the help! WOOT
 

FAQ: Curent densitys relation to drift velocity

What is current density and how is it related to drift velocity?

Current density is the measure of the amount of electric current flowing through a given area. It is directly related to the drift velocity, which is the average speed at which charged particles move in a particular direction in an electric field.

How is current density calculated?

Current density is calculated by dividing the total electric current by the cross-sectional area through which the current is flowing. It is typically measured in amperes per square meter (A/m²).

What factors affect current density?

The main factor that affects current density is the strength of the electric field. Other factors such as the type of material and its resistance, as well as the temperature, can also have an impact on current density.

How does an increase in current density affect drift velocity?

An increase in current density leads to a higher drift velocity, as more charged particles are flowing through the area. This is because a stronger electric field will cause the particles to move faster in the direction of the field.

How is current density related to the conductivity of a material?

The conductivity of a material is directly related to current density. Materials with higher conductivity will have a higher current density, as they allow for easier flow of charged particles. Inversely, materials with lower conductivity will have a lower current density.

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