What is the electric field at a distance r from an infinitely long line of charge with linear charge density λ?

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Q: What is the electric field at a distance r from an infinitely long line of charge with linear charge density λ?

Solution: The electric field due to an infinitely long line of charge is given by E = λ/(2πε₀r), directed radially outward from the line.

Steps: 6

Step 1: Understand that we have an infinitely long line of charge, which means the charge is spread out evenly along a straight line.
Step 2: Identify the linear charge density, λ, which tells us how much charge is present per unit length of the line.
Step 3: Recognize that we want to find the electric field (E) at a distance r from this line of charge.
Step 4: Use the formula for the electric field due to an infinitely long line of charge, which is E = λ/(2πε₀r).
Step 5: Note that ε₀ is the permittivity of free space, a constant that helps us calculate electric fields in vacuum.
Step 6: Understand that the direction of the electric field is radially outward from the line of charge.