Problem 1 - College Physics

Question

A pair of parallel plates is charged by a 12-V battery. If the electric field between the plates is \(1200 \mathrm{~N} / \mathrm{C}\), how far apart are the plates?

Step-by-Step Solution

Answer

The distance between the plates is 0.01 meters or 1 cm.

Step 1: Understand the Problem

We have two parallel plates with a voltage of 12 V across them, and the electric field strength between the plates is 1200 N/C. We are tasked with finding the separation distance between the plates.

Step 2: Use the Electric Field Formula

The relationship between voltage (V), electric field (E), and distance (d) between parallel plates is given by the formula: \( V = E \cdot d \). We will use this formula to find the distance \( d \).

Step 3: Rearrange the Formula

We need to solve the equation \( V = E \cdot d \) for \( d \). Rearrange the formula to get \( d = \frac{V}{E} \).

Step 4: Substitute Known Values

Substitute the known values into the rearranged formula: \( d = \frac{12 \text{ V}}{1200 \text{ N/C}} \).

Step 5: Calculate the Distance

Calculate \( d \) by performing the division: \( d = \frac{12}{1200} = 0.01 \text{ m} \).

Step 6: Convert Units if Necessary

If necessary, convert the distance from meters to other units (e.g., centimeters). In this case, \( 0.01 \text{ m} \) is equivalent to 1 cm.

Key Concepts

Understanding Parallel Plates

Parallel plates are fundamental components used frequently in physics and electrical engineering. Imagine two flat, conductive surfaces placed parallel to one another. These plates can hold an electric charge, and when a voltage is applied across them, they produce a uniform electric field in the space between.

Here's what makes parallel plates fascinating and useful:

• They create a constant electric field which is useful for calculations and experiments.
• Parallel plate systems are used in capacitors, which store electrical energy.
• The electric field between the plates is straight and uniform except at the edges.

By maintaining uniformity, they allow for simplified calculations and a clearer understanding of electrostatic principles.

Deciphering Voltage

Voltage is an essential concept in the study of electricity. Essentially, voltage is the potential difference that drives charge through an electric field. It is measured in volts (V), and you can think of it as the 'push' that moves electric charges from one point to another.

In the context of parallel plates:

• Voltage is applied across the two plates to establish an electric field between them.
• The greater the voltage, the stronger the potential energy per unit of charge.
• This potential difference is what we use to perform work on charges placed between the plates.

Understanding voltage helps learners appreciate how energy is converted into electrical potential, making it a pivotal concept in circuits and fields.

Calculating the Distance

The distance between parallel plates is a straightforward calculation once you understand the relationship between voltage, electric field strength, and distance.

To determine the distance, use the formula:

• Voltage (V) = Electric Field (E) x Distance (d)

From the above, you can rearrange the formula to solve for distance:

• Distance (d) = \( \frac{V}{E} \)

In our exercise, the voltage is 12 V and the electric field is 1200 N/C. Substituting these values gives a separation distance:

• \( d = \frac{12}{1200} = 0.01 \) meters

This simple calculation illustrates how closely linked these electrical concepts are.

Unravelling Electric Field Strength

Electric field strength is a measure of how forceful an electric field is around a charged object. It is defined as the force experienced by a unit positive charge placed in the field and is measured in newtons per coulomb (N/C).

Between parallel plates, the electric field strength plays a crucial role:

• The electric field is uniform, meaning its strength is constant between the plates.
• Field strength is directly proportional to the applied voltage and inversely proportional to the distance between plates.
• This uniform strength aids in predictable force behavior on charged particles placed within the field.

Appreciating electric field strength gives insights into how charged particles move in a field and helps solve many physics problems.