Linear Charge Density of an Infinite Line of Charge

To calculate the linear charge density of an infinite line of charge, we can use the formula:

λ = Q / L

Where:
- λ is the linear charge density (C/m)
- Q is the total charge on the line (C)
- L is the length of the line (m)

In this case, we are given the electric field produced by the line of charge at a distance of 0.02m. We can use this information to calculate the linear charge density.

Step 1: Identify the Given Information

- Electric field (E) = 9×10^9 N/C
- Distance from the line of charge (r) = 0.02m

Step 2: Calculate the Charge Density

We know that the electric field produced by an infinite line of charge is given by the formula:

E = λ / (2πε₀r)

Where:
- E is the electric field (N/C)
- λ is the linear charge density (C/m)
- ε₀ is the permittivity of free space (8.85×10^-12 C²/(N·m²))
- r is the distance from the line of charge (m)

Rearranging the formula, we can solve for λ:

λ = 2πε₀rE

Substituting the given values:

λ = 2π × 8.85×10^-12 C²/(N·m²) × 0.02m × 9×10^9 N/C

Simplifying the expression:

λ = 2 × 3.14 × 8.85×10^-12 C²/(N·m²) × 0.02m × 9×10^9 N/C

λ = 1.99×10^-10 C/m

Step 3: Interpret the Result

The linear charge density of the infinite line of charge is 1.99×10^-10 C/m. This means that for every meter of the line of charge, there is a charge of 1.99×10^-10 Coulombs.