All insulated metal bodies can store charge - Leaving Cert Physics - Question 7 - 2020

A diagram illustrating the pear-shaped conductor would show.

1. The charged object nearby.
2. Negative charges concentrated at the nearest point to the charged object and positive charges distributed on the far side.

Capacitance (C) is defined as the ability of a system to store an electric charge per unit voltage. The formula for capacitance is given by:

$C = \frac{Q}{V}$ where $Q$ is the charge stored and $V$ is the voltage across the capacitor.

The energy stored in the capacitor (E) is given by:

$E = \frac{1}{2} C V^2$ Substituting the given values: $E = \frac{1}{2} \times 4000 \times 10^{-6} F \times (500 V)^2 = 500 J$

Using the specific heat formula:

$Q = mc \Delta T$ We have,

• mass ($m$) = 0.04 kg,
• specific heat capacity ($c$) = 4180 J kg⁻¹ K⁻¹,
• energy ($Q$) = 500 J.

Rearranging for the rise in temperature ($\Delta T$):

$\Delta T = \frac{Q}{mc} = \frac{500 J}{0.04 kg \times 4180 J kg^{-1} K^{-1}} = 2.98 K$

1. Apparatus: Use a parallel-plate capacitor, a power supply, and a capacitance meter.
2. Method: Measure the capacitance at varying distances by adjusting the separation of the plates.
3. Observations: Record the capacitance values for each distance and graph them. As the distance between the plates increases, the capacitance decreases, demonstrating the inverse relationship.

To find the surface area (A) of the inner cylinder:

$A = 2 \pi r h$ where $r = 0.06 m$ and $h = 0.17 m$. Calculating: $A = 2 \pi \times 0.06 m \times 0.17 m = 0.064 m^2$

The capacitance (C) can be calculated using the formula:

$C = \varepsilon_0 \frac{A}{d}$ where:

• $\varepsilon_0$ = 8.85 × 10⁻¹² F/m,
• $A$ is the surface area calculated earlier,
• $d$ is the dielectric thickness (0.005 m). Continuing from the previous calculation, substituting values will yield: $C ≈ 44 µF$

The property of glass that allows it to be used as a dielectric is its high dielectric strength and its relative permittivity, which increases the capacitor's ability to store charge without conducting electricity.