Calculating Electric Field Distance for a Given Charge

Understanding the relationship between the electric field and the distance from a point charge is a fundamental concept in physics. This article will guide you through the process of calculating the distance from a point charge where the electric field has a specific magnitude.

Magnitude of the Electric Field

The electric field (E) created at a distance (r) from a point charge (Q) can be calculated using Coulomb's law. This formula is given by:

[E frac{kQ}{r^2}]

Key Components

(E): Electric field strength (measured in Newtons per Coulomb, N/C) (k): Coulomb's constant, approximately (8.99 times 10^9 , text{N m}^2/text{C}^2) (Q): Charge magnitude (measured in Coulombs, C) (r): Distance from the charge (measured in meters, m)

Sample Problem

Suppose you want to find the distance from a particle with a charge of (Q -3.00 , text{nC} -3.00 times 10^{-9} , text{C}) where the electric field strength (E) is 12.0 N/C. To solve this, follow these steps:

Determine the values of the known variables: (E 12.0 , text{N/C}) (Q -3.00 times 10^{-9} , text{C}) (take the absolute value for calculation) Use the formula to solve for (r)

Step-by-Step Solution

Rearrange the formula to solve for (r): [r^2 frac{kQ}{E}] [r sqrt{frac{kQ}{E}}]

Substitute the Values

Substitute (k 8.99 times 10^9 , text{N m}^2/text{C}^2), (Q 3.00 times 10^{-9} , text{C}), and (E 12.0 , text{N/C}) into the equation:

[r sqrt{frac{8.99 times 10^9 , text{N m}^2/text{C}^2 times 3.00 times 10^{-9} , text{C}}{12.0 , text{N/C}}}]

Calculate the Numerator

[8.99 times 10^9 , text{N m}^2/text{C}^2 times 3.00 times 10^{-9} , text{C} 26.97 , text{N m}^2/text{C}]

Solve for (r)

[r sqrt{frac{26.97 , text{N m}^2/text{C}}{12.0 , text{N/C}}}] sqrt{2.2475 , text{m}^2}] approx 1.50 , text{m}]

Therefore, the distance from the particle where the electric field has a magnitude of 12.0 N/C is approximately 1.50 meters.

Conclusion

In conclusion, understanding the relationship between the electric field and the distance from a point charge is crucial in physics. By applying Coulomb's law, you can calculate the distance from a charge where the electric field has a specific magnitude, as demonstrated in the sample problem.

Keywords: electric field, point charge, Coulomb's law, electric field strength