Multiple Choice
Two circular plates of radius 2cm are brought together so their separation is 5mm. What is the capacitance of these plates?
26. Capacitors & Dielectrics
Parallel Plate Capacitors
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A parallel plate capacitor consists of two circular plates of radius 12 cm separated by . What is the electric field strength inside the capacitor when the plates carry a charge of ?
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Verified step by step guidance1
First, understand that the electric field (E) inside a parallel plate capacitor is given by the formula: E = \( \frac{\sigma}{\varepsilon_0} \), where \( \sigma \) is the surface charge density and \( \varepsilon_0 \) is the permittivity of free space (\( 8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2 \)).
Calculate the surface charge density \( \sigma \) using the formula: \( \sigma = \frac{Q}{A} \), where Q is the charge on the plates (14 \( \mu \text{C} \) or \( 14 \times 10^{-6} \text{ C} \)) and A is the area of one plate.
Determine the area A of one circular plate using the formula: \( A = \pi r^2 \), where r is the radius of the plate (12 cm or 0.12 m).
Substitute the values of Q and A into the formula for \( \sigma \) to find the surface charge density.
Finally, substitute the value of \( \sigma \) and \( \varepsilon_0 \) into the formula for E to calculate the electric field strength inside the capacitor.
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