Final answer:
To calculate the electric field generated at the origin by a charge q1, use Coulomb's law with the constant k, the magnitude of the charge q1, and the distance from the charge to the point of measurement.
Step-by-step explanation:
Calculating the Electric Field at the Origin
To determine the electric field generated by a charge q1 at the origin, we use Coulomb's law, which defines the electric field E due to a point charge. The formula to calculate the electric field E₁ due to charge q1 is given by:
E₁ = k * |q1| / r²
where:
- k is the Coulomb's constant (approximately 8.99 x 10⁹ N*m²/C²),
- |q1| is the magnitude of the charge,
- r is the distance from the charge to the point where we're measuring the field.
In this scenario, with a charge q1 of 5.00×10⁻⁹ C and a distance of 2.00×10⁻² m, we can substitute these values into the formula:
E₁ = (8.99 x 10⁹ N*m²/C²) * (5.00×10⁻⁹ C) / (2.00×10⁻² m)²
Upon solving, you can calculate the numerical value of the electric field at the origin due to charge q1.