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Electric force is a fundamental concept in physics, describing the attractive or repulsive interaction between charged particles. This force arises from electric fields, which are regions of space around a charge where other charges experience a force. The magnitude of the force can be calculated using the formula:

• Electric force: \( F_{electric} = q \times E \)

Here, \( q \) is the charge of the particle experiencing the force, and \( E \) is the electric field's strength. The direction of the electric force depends on the charge's sign and field direction.
In scenarios where two forces interact, like in the original exercise, the electric force may counteract other forces, such as gravity. In our example, to keep a particle stationary, the electric force must be equal and opposite to the gravitational force acting downward. This makes electric force both a practical tool in balancing and manipulating charges within a given field.

Gravitational force is the force of attraction between two masses due to their masses and the distance between them. This is mathematically represented as:

• Gravitational force: \( F_{gravity} = m \times g \)

In this formula, \( m \) is the mass of the object experiencing the force, and \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \) on Earth's surface.
This force points towards the center of the mass generating it, typically Earth's center for objects near its surface. The original exercise asks us to consider this downward force acting on a small particle. To keep the particle stationary, the problem becomes a balance of forces where gravitational force and electric force must neutralize each other. This setup is common in physics to understand scenarios where multiple forces act simultaneously.

Charge calculation is critical in solving problems involving electric fields. In our exercise, we need to determine the charge required to balance a 1.3 g particle in an electric field of 650 N/C. To find the charge, rearrange the equation for electric force to:

• \( q = \frac{F_{gravity}}{E} \)

From the gravitational force calculation, \( F_{gravity} = 0.0013 \, \text{kg} \times 9.81 \, \text{m/s}^2 \). Then using this result and plugging it into our charge equation with \( E = 650 \, \text{N/C} \), gives us the charge magnitude.
Additionally, the problem specifies that the electric field is downward; hence, for the electric force to act upwards and counteract gravity, a negative charge is necessary. This is because the force direction is opposite to the field direction when the charge is negative.