A 3.0-cm-diameter parallel-plate capacitor has a 2.0 mm spacing. The electric field strength inside the capacitor is 1.0×10^5 V/m. b. How much charge is on each plate?

Verified step by step guidance

1. Calculate the area of the capacitor plates using the formula for the area of a circle, $A=\pi r^2$, where $r$ is the radius of the plates. Convert the diameter to radius by dividing by 2, and ensure the radius is in meters.
2. Use the formula for the capacitance of a parallel-plate capacitor, $C={ϵ}_0\frac{A}{d}$, where ${ϵ}_0$ is the permittivity of free space (approximately $8.85\times {10}^{-12}$ Farad/meter), $A$ is the area calculated in the previous step, and $d$ is the separation between the plates in meters.
3. Calculate the potential difference (voltage) across the plates using the relation $V=E\times d$, where $E$ is the electric field strength and $d$ is the separation between the plates.
4. Use the formula $Q=C\times V$ to find the charge on each plate, where $C$ is the capacitance calculated earlier and $V$ is the voltage across the plates.
5. Ensure all units are consistent (meters for distance, Farads for capacitance, Volts for voltage) throughout the calculations to get the correct value for the charge in Coulombs.

Key Concepts

Capacitance

Capacitance is a measure of a capacitor's ability to store charge per unit voltage. It is defined as C = Q/V, where C is capacitance, Q is the charge stored, and V is the voltage across the plates. For parallel-plate capacitors, capacitance can also be calculated using the formula C = ε₀(A/d), where ε₀ is the permittivity of free space, A is the area of one plate, and d is the separation between the plates.

Electric Field

The electric field (E) in a capacitor is the force per unit charge experienced by a positive test charge placed in the field. It is uniform between the plates of a parallel-plate capacitor and is given by E = V/d, where V is the voltage and d is the distance between the plates. The strength of the electric field is crucial for determining the potential difference and the charge on the plates.

Charge on Plates

The charge (Q) on each plate of a capacitor can be calculated using the relationship Q = C × V. Once the capacitance is determined from the physical dimensions and the electric field strength, and the voltage is derived from the electric field and plate separation, the total charge can be computed. This charge is equal in magnitude but opposite in sign on the two plates, leading to the storage of electrical energy in the capacitor.