What is the electric field at a distance d from an infinitely long charged wire

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Question: What is the electric field at a distance d from an infinitely long charged wire with linear charge density λ?

Options:

Correct Answer: λ/(2πε₀d)

Solution:

The electric field due to an infinitely long charged wire is given by E = λ/(2πε₀d).

What is the electric field at a distance d from an infinitely long charged wire with linear charge density λ?

What is the electric field at a distance d from an infinitely long charged wire with linear charge density λ?

Step 1: Understand that we have an infinitely long wire that is charged. This means it has a charge distributed along its length.
Step 2: Identify the linear charge density, λ, which tells us how much charge is present per unit length of the wire.
Step 3: Recognize that we want to find the electric field (E) at a certain distance (d) from the wire.
Step 4: Recall the formula for the electric field due to an infinitely long charged wire, which is E = λ/(2πε₀d).
Step 5: In this formula, ε₀ is a constant called the permittivity of free space, which is a value that helps us calculate electric fields in vacuum.
Step 6: Plug in the values of λ (linear charge density) and d (distance from the wire) into the formula to find the electric field.

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