Current and Current Density

In summary, the current in a cylindrical conductor with varying current density is calculated by finding the integral of jdA from 0 to R, resulting in (1/2)jopiR^3. However, when the current density is reversed, the integral results in a different answer of (1/6)jopiR^3, indicating a mistake in the calculation. To find the correct result, dA should be defined as an infinitesimal ring.
  • #1
Destrio
212
0
a) The current density across a cylindrical conductor of radius R varies according tot he equation j = jo(1-r/R)
where r is the distance from the axis. Thus the current density is a maximum jo at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current in terms of jo and the conductor's cross sectional area A = piR^2

so i took i = integral from 0 to R of jdA
i = jopiR^2(r-r^2/2R) |(0,R)
i = jopiR^2(R-(R/2) = (1/2)jopiR^3

b) Suppose that instead the current density is a maximum jo at the surface and decreases linearly to zero on the axis, so that
j = jor/R

so i did the same thing and got
i=jopiR(R^2/2) = (1/2)jopiR^3

Why is the result different from a?
I realized at this point in the question that I must have made a mistake, as I got the same result from b as i did in a

Thanks
 
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  • #2
anyone?
 
  • #3
You may want to try making dA an infinitesimal ring so that dA = 2(Pi)(r)(dr) I believe you will get something like 1/2 and 1/6 R^2
 

What is current?

Current is the flow of electric charge, typically measured in amperes (A). It is the rate at which electric charge passes through a given point in a circuit.

What is the difference between direct current (DC) and alternating current (AC)?

DC is a type of current that flows in only one direction, while AC is a type of current that periodically reverses direction. Most electronic devices use DC, while AC is used for power transmission over long distances.

What is current density?

Current density is a measure of the amount of current flowing through a given area. It is calculated by dividing the current (I) by the cross-sectional area (A) that the current is passing through.

What factors affect current density?

The two main factors that affect current density are the magnitude of the current and the cross-sectional area through which the current is flowing. Other factors that can impact current density include temperature, the material through which the current is flowing, and the presence of any resistors in the circuit.

Why is current density an important concept in electricity?

Current density is an important concept because it helps us understand how electric current flows through different materials and how it is affected by different factors. It is also essential in practical applications, such as designing circuits and determining the proper sizing of wires and other components to handle a given amount of current.

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