91Ó°ÊÓ

The concept of potential difference, often referred to as voltage, is central to understanding electric fields. It is defined as the amount of work needed to move a charge between two points in an electric field.
In the context of two parallel plates, the potential difference between the plates is the driving factor for the electric field that is established.

• The potential difference is measured in volts (V), and provides a measure of the energy difference per unit charge between the two points.
• In this scenario, the potential difference of 360 V is distributed uniformly across the separation of 45 mm between the plates.
• This uniform distribution allows us to assume that the electric field between the plates is uniform too.

Understanding potential difference helps us to calculate the electric field strength, as described by the formula:
\[ E = \frac{V}{d} \]
This simple formula is essential for determining how strong the electric field is and is crucial when trying to calculate the force on a charge placed in such a field.

The force on a charge within an electric field can be determined using the relationship between the charge, the electric field, and the force exerted.
In a uniform electric field, such as the one between the two metal plates, this force can be calculated by the formula:
\[ F = qE \]
where:

• \( F \) is the force in newtons (N)
• \( q \) is the charge in coulombs (C)
• \( E \) is the electric field strength in volts per meter (V/m)

For a charge of +2.40 nC (nanocoulombs) in a field of 8000 V/m, this results in a force of:

• \( F = 2.40 \times 10^{-9} \times 8000 \)
• This gives a force of \( F = 1.92 \times 10^{-5} \text{ N} \)

The significance of knowing the force on a charge is that it tells us how the electric field affects charged particles, which is fundamental when analyzing electric circuits and fields.

Work done by an electric field refers to the energy transfer that occurs when a charge moves within the field.
The work done by the field can be calculated using the formula:
\[ W = q \Delta V \]
where:

• \( W \) is the work in joules (J)
• \( q \) is the charge in coulombs (C)
• \( \Delta V \) is the potential difference in volts (V)

In our specific example, the work done is:

• With a charge of +2.40 nC and a potential difference of 360 V, we have: \( W = 2.40 \times 10^{-9} \times 360 \)
• This results in \( W = 8.64 \times 10^{-7} \text{ J} \)

Understanding this concept is crucial because it connects the physical movement of charges to the potential energy changes within the field. This relationship is a fundamental aspect of electrical physics, explaining how energy is harvested and utilized in electric fields.

The electric potential energy of a system refers to the potential an object has to do work due to its position within an electric field.
When a charge moves in an electric field, its electric potential energy changes, and is quantified by:\[ \Delta U = q \Delta V \]
This change in potential energy equals the work done by the electric field, thus:

• The change in potential energy, \( \Delta U \)
• Is the same as the work done, \( W = 8.64 \times 10^{-7} \text{ J} \)

This means that as the charge moves from a higher potential to a lower potential, the field performs work on the charge, showing a direct conversion of potential energy into work.
In practical terms, calculating the change in electric potential energy helps in understanding how electric fields store and transfer energy, and is key to the study of electricity and circuits.