How much energy is stored by the electric field between two square plates, 9.3  cm
  on a side, separated by a 1.7- mm air gap? The charges on the plates are equal and opposite and of magnitude 14  nC.

The energy stored by the electric field between two parallel plates can be calculated using the formula for the energy stored in a capacitor:

\[
U = \frac{1}{2} C V^2
\]

However, we need to determine both the capacitance \( C \) and the voltage \( V \). 

### Step 1: Capacitance of a Parallel Plate Capacitor
The capacitance of a parallel plate capacitor is given by:

\[
C = \frac{\varepsilon_0 A}{d}
\]

Where:
- \( \varepsilon_0 \) is the permittivity of free space (\( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \))
- \( A \) is the area of one of the plates
- \( d \) is the separation between the plates

Given:
- Plate side length = \( 9.3 \, \text{cm} = 0.093 \, \text{m} \), so the area \( A = (0.093)^2 \, \text{m}^2 \)
- Distance between plates \( d = 1.7 \, \text{mm} = 1.7 \times 10^{-3} \, \text{m} \)

### Step 2: Voltage Across the Plates
The voltage across the plates can be determined from the relationship between charge, capacitance, and voltage:

\[
Q = C V
\]

So,

\[
V = \frac{Q}{C}
\]

Where:
- \( Q = 14 \, \text{nC} = 14 \times 10^{-9} \, \text{C} \)

### Step 3: Energy Stored
Once we have \( C \) and \( V \), we can use the energy formula:

\[
U = \frac{1}{2} C V^2 = \frac{Q^2}{2C}
\]

Let's calculate these step-by-step.The energy stored by the electric field between the two square plates is approximately \( 2.18 \, \mu\text{J} \) (microjoules).

Would you like further details on the process, or do you have any questions?

Here are some related questions to expand your understanding:
1. How does the distance between the plates affect the stored energy?
2. What is the effect of increasing the plate area on the capacitance?
3. How would the energy change if the medium between the plates was not air but a dielectric material?
4. How can we calculate the electric field strength between the plates?
5. What happens to the stored energy if the charge on the plates is doubled?

**Tip:** The energy stored in a capacitor is proportional to the square of the voltage across it, meaning even small increases in voltage significantly boost the energy stored.

How much energy is stored by the electric field between two square plates, 9.3 cm on a side, separated by a 1.7-mm air gap? The charges on the plates are equal and opposite and of magnitude 14 nC.

Calculate the energy stored by the electric field between two parallel plate capacitors of 9.3 cm sides and a 1.7 mm air gap. Given a charge of 14 nC, this detailed solution explores key concepts in electromagnetism, including capacitance, electric field, and energy storage in capacitors.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation