BridgeElectricityFree

The Open-Evening Capacitor

Capacitors, dielectrics, RC, energy

For a school open evening, a student builds a large parallel-plate capacitor from two square aluminium plates of side

12.0\ \text{cm}

, held parallel and

d = 2.00\ \text{mm}

apart in air. The plates stay connected to a

9.00\ \text{V}

battery throughout. A glass slab of dielectric constant

\kappa = 4.50

, with the same area as the plates and thickness

t = 1.50\ \text{mm}

, can be slid into the gap so that it covers the whole plate area, leaving a total air gap of thickness

d - t

. Treat the field between the plates as uniform, ignore edge effects, and take the dielectric constant of air as

1.00

Data: ε₀ = 8.85 × 10⁻¹² F m⁻¹

(a)

calculate1 mark

Calculate the capacitance

C_0

of the empty capacitor and the charge

Q_0

on its positive plate.

(b)

show that2 marks

Show that, with the slab fully inserted, the capacitance is

C = \dfrac{\varepsilon_0 A}{d - t + t/\kappa}

(c)

calculate2 marks

Calculate the new capacitance, and the extra charge that flows from the battery as the slab is inserted.

(d)

explain3 marks

Stating what stays constant, explain why the electric field strength in the remaining air gap increases when the slab is inserted, and calculate its value before and after. Then state and explain the limiting value of

C

\kappa \to \infty

Your score: 0 / 8(0 of 4 parts marked — open “Mark it” on each part)