Assume this 1.20-mm-radius copper wire is electrically neutral in the earth reference frame, in which it is at rest and carrying a current. calculate the linear charge density λ′ of the copper wire in a reference frame moving along with the electrons if the electrons are moving at 5.20 ×10−4m/s .

The charge density in the system is

Explanation:

To solve this problem it is necessary to keep in mind the concepts related to current and voltage through the density of electrons in a given area, considering their respective charge.

Our data given correspond to:

We need to asume here the number of free electrons in a copper conductor, at which is generally of

The equation to find the current is

Where

I =Current

V=Velocity

A = Cross-Section Area

e= Charge for a electron

n= Number of free electrons

Then replacing,

Now to find the linear charge density, we know that

Where:

I: current intensity

Q: total electric charges

t: time in which electrical charges circulate through the conductor

And also that the velocity is given in proportion with length and time,

The charge density is defined as

Replacing our values

Therefore the charge density in the system is

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