Calculate The Electric Field at The Position 1.87m 0 Chegg

Introduction

The electric field at a point in space is a vector quantity that describes the force experienced by a unit positive charge placed at that point. Calculating the electric field at a specific position is fundamental in understanding electrostatics.

In this guide, we'll focus on calculating the electric field at the position (1.87 m, 0) due to a point charge. This is a common scenario in physics problems and laboratory experiments.

Formula

Coulomb's Law provides the foundation for calculating the electric field. The electric field (E) at a distance r from a point charge q is given by:

For multiple charges, the electric field at a point is the vector sum of the fields due to each individual charge.

Example Calculation

Let's calculate the electric field at position (1.87 m, 0) due to a +2.0 μC charge located at the origin (0, 0).

1. Convert the charge to coulombs: 2.0 μC = 2.0 × 10⁻⁶ C
2. Calculate the distance from the origin to (1.87 m, 0): r = 1.87 m
3. Plug values into the formula:
   E = (8.99 × 10⁹ N·m²/C²) × (2.0 × 10⁻⁶ C) / (1.87 m)²
4. Calculate the denominator: (1.87 m)² = 3.4969 m²
5. Calculate the numerator: (8.99 × 10⁹) × (2.0 × 10⁻⁶) = 17.98 × 10³ N·m²/C
6. Divide to find E: 17.98 × 10³ / 3.4969 ≈ 5142.5 N/C

The electric field at (1.87 m, 0) is approximately 5142.5 N/C directed away from the charge.

Interpreting Results

The electric field value indicates the force that would be experienced by a unit positive charge placed at that point. A higher electric field means a greater force would be exerted on a test charge.

In practical terms:

• Fields greater than 3 × 10⁶ N/C can cause dielectric breakdown in air
• Fields around 10⁵ N/C are typical for lightning
• Fields less than 10⁴ N/C are common in everyday situations