What is the relationship between electric field and the distance between the point charge and a specific point in space?
1 Answer
The electric field (E) created by a point charge has an inverse relationship with the square of the distance (r) from the point charge to a specific point in space. This relationship is described by Coulomb's Law, which states:
\[
E = \frac{k \cdot |Q|}{r^2}
\]
Where:
Key points to note:
In summary, the electric field due to a point charge gets weaker as you move farther from the charge. The relationship is such that if you increase the distance, the electric field strength decreases rapidly by a factor of \(r^2\).
\[
E = \frac{k \cdot |Q|}{r^2}
\]
Where:
- \(E\) is the electric field at a point in space,
- \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\)),
- \(Q\) is the magnitude of the point charge,
- \(r\) is the distance from the point charge to the point where the electric field is being measured.
Key points to note:
- Inverse Square Law: The electric field strength decreases as the distance from the point charge increases. Specifically, if the distance doubles, the electric field strength becomes one-fourth of what it was at the original distance.
- Direction of the Electric Field: The electric field points away from a positive charge and toward a negative charge. The direction depends on the sign of the charge.
In summary, the electric field due to a point charge gets weaker as you move farther from the charge. The relationship is such that if you increase the distance, the electric field strength decreases rapidly by a factor of \(r^2\).