<h2>
Complete Question:</h2>
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?
<h2>
Answer:</h2>
5.02 x 10¹¹
<h2>
Explanation:</h2>
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
<em>From the question;</em>
E = 3 x 10⁶N/C
A = 5.5cm x 5.5cm = 30.25cm² = 0.003025m²
<em>Substitute these values into equation (i) as follows;</em>
3 x 10⁶ = Q / (0.003025 x 8.85 x 10⁻¹²)
<em>Solve for Q;</em>
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]
<em>Substitute these values into equation (ii) as follows;</em>
8.03 x 10⁻⁸ = N x 1.6 x 10⁻¹⁹
<em>Solve for N;</em>
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
