Question

Енергія електричного поля конденсатора , поміщеного у гас 2, 4 мкДж. Визначити площу пластини, розміщених на відстані 1 мм, якщо конденсатор зарядили до напруги у 160 В?

Answer 1

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Answer 2

Calculating the Area of the Capacitor Plate

To calculate the area of the capacitor plate, we can use the formula for the energy stored in a capacitor and the formula for the capacitance of a parallel plate capacitor.

The energy stored in a capacitor can be calculated using the formula:

E = (1/2) * C * V^2

Where: - E = energy stored in the capacitor (in joules) - C = capacitance of the capacitor (in farads) - V = voltage across the capacitor (in volts)

The capacitance of a parallel plate capacitor is given by the formula:

C = (ε * A) / d

Where: - C = capacitance (in farads) - ε = permittivity of the material between the plates - A = area of the plates (in square meters) - d = distance between the plates (in meters)

We are given: - Energy stored in the capacitor, E = 2.4 μJ = 2.4 * 10^-6 J - Voltage across the capacitor, V = 160 V - Distance between the plates, d = 1 mm = 0.001 m

First, we can use the energy formula to find the capacitance C, and then use the capacitance formula to solve for the area A.

Calculating the Capacitance

Using the energy formula, we can solve for the capacitance C:

E = (1/2) * C * V^2

C = 2 * E / V^2

Substitute the given values: C = 2 * (2.4 * 10^-6 J) / (160 V)^2

Calculating the Area

Now, we can use the capacitance formula to solve for the area A:

C = (ε * A) / d

Solving for A: A = (C * d) / ε

Where ε is the permittivity of the material between the plates. Since the specific material is not provided, we'll assume a vacuum, where ε is approximately 8.85 * 10^-12 F/m.

Substitute the values: A = (C * d) / ε

After calculating A, we will have the area of the capacitor plate.

Let's calculate the values and find the area of the capacitor plate.