Question

Two circular disks spaced 0.50 mm apart form a parallel-plate capacitor. Transferring 3.50×10⁹ electrons from one disk to the other causes the electric field strength to be 3.00×10⁵ N/C. What is the capacitance of the parallel-plate capacitor?

Answer 1

To find the capacitance of the parallel-plate capacitor, use the formula C = Q / V, where C is the capacitance, Q is the charge on the plates, and V is the potential difference between the plates. Given the electric field strength and the number of electrons transferred, calculate the charge and substitute it into the capacitance formula to find the capacitance of the parallel-plate capacitor.

Step-by-step explanation:

To find the capacitance of the parallel-plate capacitor, we can use the formula:

C = Q / V

Where:

• C is the capacitance
• Q is the charge on the plates
• V is the potential difference between the plates

Given that the electric field strength is 3.00×10⁵ N/C and we are transferring 3.50×10⁹ electrons, we can calculate the charge:

Q = charge of one electron × number of electrons transferred

Q = (1.60×10⁻¹⁹ C) × (3.50×10⁹ electrons)

Now we can substitute the values into the capacitance formula:

C = (1.60×10⁻¹⁹ C × 3.50×10⁹ electrons) / (3.00×10⁵ N/C)

Simplifying, we get:

C = 5.93 × 10⁻²³ F

Therefore, the capacitance of the parallel-plate capacitor is 5.93 × 10⁻²³ F.