The linear charge density of an infinite wire can be any value, depending on the amount of charge distributed along its length. The referenced material gives one example: λ = 4 x 105 C/m.
Here's a breakdown:
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Linear Charge Density (λ): This represents the amount of electric charge per unit length, typically measured in Coulombs per meter (C/m).
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Infinite Wire: The "infinite" nature is a theoretical simplification. It allows us to ignore edge effects and apply simpler formulas for calculating electric fields. In practical situations, it refers to wires whose length is much greater than the distance at which the electric field is being measured.
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The Value of λ: The specific value of the linear charge density depends on how much charge is present on the wire. If the wire is uncharged (neutral), then λ = 0 C/m. In the provided reference, λ = 4 x 105 C/m, indicating a substantial positive charge distributed along the wire.
In summary, while the concept of linear charge density for an infinite wire is constant along the wire's length, the value of that density can vary greatly depending on the amount of charge present. The reference provides a specific example of a value, but it is not a universal constant.
