what is the equation for the electric field from a distance away from a charged line of infinite length

The electric field \( E \) due to a uniformly charged line of infinite length at a perpendicular distance \( r \) from the line is given by the equation:

\[
E = \frac{\lambda}{2 \pi \epsilon_0 r}
\]

where:
- \( E \) is the magnitude of the electric field,
- \( \lambda \) is the linear charge density (charge per unit length) of the line,
- \( \epsilon_0 \) is the permittivity of free space (\( \epsilon_0 \approx 8.854 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 \)),
- \( r \) is the perpendicular distance from the line to the point where the field is being calculated.

This equation is derived by applying Gauss's Law to an infinite line of charge, assuming cylindrical symmetry.

Would you like further details on the derivation or have any questions?

Here are 5 related questions to consider:
1. How is the electric field affected if the line charge is not infinite but finite?
2. What happens to the electric field when the distance from the line doubles?
3. How does the electric field change if the linear charge density \( \lambda \) increases?
4. How can Gauss's Law be applied to other geometries, like spherical or planar charge distributions?
5. What is the direction of the electric field produced by an infinite line charge?

**Tip:** When using this formula, remember that the electric field points radially outward from a positively charged line and radially inward toward a negatively charged line.

What is the equation for the electric field from a distance away from a charged line of infinite length?

Discover the equation for calculating the electric field at a distance from an infinitely long charged line. Learn how Gauss's Law is applied in cylindrical symmetry to derive the electric field formula: E = λ / (2 π ε₀ r). Understand key concepts in electromagnetism, such as linear charge density, and explore related questions about field behavior for different charge distributions.

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