Question

Air "breaks down" when the electric field strength reaches 3 × 106 n/c, causing a spark. A parallel-plate capacitor is made from two 5.5 cm × 5.5 cm electrodes.

Answer 1

Electric field between the plates of parallel plate capacitor is given as

$E = \frac{Q}{A\epsilon_0}$

here area of plates of capacitor is given as

$A = 0.055 * 0.055$

$A = 3.025 * 10^{-3}$

also the maximum field strength is given as

$E = 3 * 10^6 N/C$

now we will plug in all data to find the maximum possible charge on capacitor plates

$3 * 10^6 = \frac{Q}{3.025 * 10^{-3}*8.85 * 10^{-12}}$

$Q = 8.03 * 10^{-8} C$

so the maximum charge that plate will hold will be given by above

Answer 2

Complete Question:

Air "breaks down" when the electric field strength reaches 3×10⁶N/C, causing a spark. A parallel-plate capacitor is made from two 5.5cm × 5.5cm plates.  

How many electrons must be transferred from one disk to the other to create a spark between the disks?

Answer:

5.02 x 10¹¹

Explanation:

The electric field E of a parallel-plate capacitor is given by;

E = Q / (A ε₀)        --------------------------(i)

Where;

Q = the charge on the plates

A = Area of any of the plates

ε₀ = electric constant =  8.85 x 10⁻¹²F/m

From the question;

E = 3 x 10⁶N/C

A = 5.5cm x 5.5cm = 30.25cm² = 0.003025m²

Substitute these values into equation (i) as follows;

3 x 10⁶ = Q / (0.003025 x 8.85 x 10⁻¹²)

Solve for Q;

Q = 3 x 10⁶ x 0.003025 x 8.85 x 10⁻¹²

Q = 8.03 x 10⁻⁸

The charge on the capacitor is therefore, 8.03 x 10⁻⁸C

Now, to get the number of electrons that must be transferred from one disk to the other to create a spark between the disks, we use the relation;

Q = N x E               ----------------------(ii)

Where;

Q = the charge = 8.03 x 10⁻⁸C                            [as calculated above]

N = the number of electrons

E = the charge of one electron = 1.6 x 10⁻¹⁹C    [a known value]

Substitute these values into equation (ii) as follows;

8.03 x 10⁻⁸ = N x 1.6 x 10⁻¹⁹

Solve for N;

N = [8.03 x 10⁻⁸] / [1.6 x 10⁻¹⁹]

N = 5.02 x 10¹¹

Therefore, the number of electrons that must be transferred from one disk to the other to create a spark between the disks is 5.02 x 10¹³