## Electric Force Between Charged Spheres

Imagine two tiny spheres, each carrying an equal amount of electric charge. Suspend them in space, separated by a mere 20.0 centimeters. An invisible force exists between them, pulling them together or pushing them apart depending on the nature of their charges. This phenomenon is known as electrostatic force, and it plays a crucial role in various aspects of science and technology.

Understanding the behavior of charged spheres is essential for grasping concepts in electrostatics, electronics, and many other fields. But before delving into the intricacies of this topic, let’s explore some of the common challenges faced when studying electrostatics. These challenges often stem from difficulties visualizing the abstract nature of electric fields and forces, as well as the complex interactions between multiple charges.

The key to unlocking the mysteries of charged spheres lies in understanding the fundamental principles governing their behavior. The electrostatic force between two spheres is directly proportional to the magnitude of their charges and inversely proportional to the square of the distance between them. This relationship is mathematically expressed by Coulomb’s law, which provides a quantitative framework for predicting the strength and direction of the force.

In our example of two spheres spaced 20.0 centimeters apart, the electrostatic force can be calculated using Coulomb’s law. By knowing the magnitude and sign of the charges, we can determine whether the force is attractive or repulsive. This knowledge is crucial for understanding the behavior of charged particles in various systems, such as ion propulsion in spacecraft or the operation of particle accelerators.

## Two Small Spheres Spaced 20.0 Centimeters Apart Have Equal Charge

### Electrostatic Force between Charged Spheres

The electrostatic force between two charged spheres is directly proportional to the product of the charges on the spheres and inversely proportional to the square of the distance between their centers. This relationship is expressed by Coulomb’s law:

```
F = k * q1 * q2 / r^2
```

where:

- F is the electrostatic force (in newtons)
- k is Coulomb’s constant (8.988 × 10^9 N⋅m^2/C^2)
- q1 and q2 are the charges on the spheres (in coulombs)
- r is the distance between the centers of the spheres (in meters)

### Problem Statement

Two small spheres, each with a charge of q, are spaced 20.0 centimeters apart. Calculate the electrostatic force between the spheres.

### Solution

To solve this problem, we will use Coulomb’s law. The charges on the spheres are equal, so we can write q1 = q2 = q. The distance between the spheres is 20.0 centimeters, or 0.200 meters. Substituting these values into Coulomb’s law, we get:

```
F = k * q^2 / r^2
```

```
F = (8.988 × 10^9 N⋅m^2/C^2) * q^2 / (0.200 m)^2
```

```
F = 2.247 × 10^11 N⋅m^2/C^2 * q^2
```

Therefore, the electrostatic force between the spheres is 2.247 × 10^11 N⋅m^2/C^2 multiplied by the square of the charge on each sphere.

### Calculations with Specific Charge Values

**Case 1: q = 1 microcoulomb (μC)**

```
F = 2.247 × 10^11 N⋅m^2/C^2 * (1 × 10^-6 C)^2
```

```
F = 224.7 N
```

**Case 2: q = 10 microcoulombs (μC)**

```
F = 2.247 × 10^11 N⋅m^2/C^2 * (10 × 10^-6 C)^2
```

```
F = 22470 N
```

### Conclusion

The electrostatic force between two small spheres spaced 20.0 centimeters apart is directly proportional to the square of the charge on each sphere. The larger the charge, the greater the force. The force is also inversely proportional to the square of the distance between the spheres.

## FAQs

**What is the electrostatic force between two spheres with opposite charges?**

The electrostatic force between two spheres with opposite charges is attractive. This means the spheres will move towards each other.

**What is the electrostatic force between two spheres with the same charge?**

The electrostatic force between two spheres with the same charge is repulsive. This means the spheres will move away from each other.

**How does the distance between the spheres affect the electrostatic force?**

The electrostatic force is inversely proportional to the square of the distance between the spheres. This means that as the distance between the spheres increases, the electrostatic force decreases.

**What is Coulomb’s law?**

Coulomb’s law is an equation that describes the electrostatic force between two charged particles. The equation is:

```
F = k * q1 * q2 / r^2
```

where:

- F is the electrostatic force (in newtons)
- k is Coulomb’s constant (8.988 × 10^9 N⋅m^2/C^2)
- q1 and q2 are the charges on the particles (in coulombs)
- r is the distance between the particles (in meters)

**What is the SI unit of charge?**

The SI unit of charge is the coulomb (C). One coulomb is equal to the charge carried by 6.2415 × 10^18 electrons.

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