Answer:
Given Parameters:
- Distance (d) = 1.2 mm = 1.2 × 10-³ m
- Side (a) = 6 cm = 6 × 10-² m
- Charge (Q) = 300 μC = 300 × 10-⁶ C
To Find :
- Energy stored between the two plates.
Solution:
[tex]\footnotesize\longrightarrow\: \sf E_{(Total \: Stored \: Energy)} = \dfrac{Q^2}{2C} \\ [/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{Q^2}{2 \bigg \{ \frac{A\epsilon_0 }{d} \bigg \}} \qquad \: \bigg \lgroup \because \rm \: C = \dfrac{A \epsilon_0}{d} \bigg \rgroup\\ [/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{Q^2d}{2A\epsilon_0}[/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{(300 \times {10}^{ - 6})^{2} 1.2 \times 10^{ - 3} }{2 \times 6 \times {10}^{ - 2} \times 6 \times {10}^{ - 2} \times 8.85 \times {10}^{ - 12} }\qquad \: \bigg \lgroup \because \rm \: \epsilon_0 = 8.85 \times {10}^{ - 12} \: C^2/Nm^2 \bigg \rgroup[/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{9 \times {10}^{4} \times {10}^{ - 12} \times 1.2 \times 10^{ - 3} }{2 \times 36\times {10}^{ - 4} \times 8.85 \times {10}^{ - 12}} \\ [/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{108 \times {10}^{ - 1} \times {10}^{4} \times {10}^{ - 12} \times 10^{ - 3} }{72\times {10}^{ - 4} \times 8.85 \times {10}^{ - 12}} \\ [/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{108 \times \cancel{{10}^{ - 12} } }{72\times {10}^{ - 4} \times 885 \times {10 }^{ - 2} \times \cancel{ {10}^{ - 12}}} \\[/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{108 }{6372 \times 10^{1} \times {10}^{ - 6}}[/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{108 }{6372 \times {10}^{ - 5}}[/tex]
[tex]\footnotesize\longrightarrow \:\sf E_{(Total \: Stored \: Energy)} = \dfrac{108 \times {10}^{5} }{6372 } \\ [/tex]
[tex]\footnotesize\longrightarrow \: \underline{\underline{\sf E_{(Total \: Stored \: Energy)} \approx0.016\times {10}^{5} \: J}}\\ [/tex]
