What is the value of 1/4 π ε₀?

The value of \( \frac{1}{4 \pi \varepsilon_0} \) is a fundamental constant in physics, particularly in electromagnetism. Here, \( \varepsilon_0 \) represents the permittivity of free space, which is approximately \( 8.854 \times 10^{-12} \, \text{F/m} \) (farads per meter).

Calculating the Value

To find \( \frac{1}{4 \pi \varepsilon_0} \), you can use the following steps:

• First, calculate \( 4 \pi \):
• Then, multiply that result by \( \varepsilon_0 \).
• Finally, take the reciprocal of the product.

Numerical Result

When you perform the calculation, you get:

Value: Approximately \( 8.9875 \times 10^9 \, \text{N m}^2/\text{C}^2 \)

Significance in Physics

This constant is crucial in Coulomb's law, which describes the force between two charged objects. It helps in understanding electric fields and forces in various applications, from simple circuits to complex electromagnetic systems.