A flat capacitor consists of round plates with a diameter of d = 16 cm, the distance between which is x = 4.0 mm.

A flat capacitor consists of round plates with a diameter of d = 16 cm, the distance between which is x = 4.0 mm. Between the plates there is an interlayer with a dielectric constant E = 5.0. The capacitor is charged to a voltage U, the charge on its plates is q = 7.4 nC. Determine the voltage of the capacitor.

To find out the voltage across the specified capacitor, we use the formula: U = q / C = q * x / (ε0 * ε * S) = 4q * x / (ε0 * ε * Π * d2).
Const: ε0 – electrical constant (ε0 = 8.85 * 10 ^ -12 F / m).
Data: q is the charge on the plates (q = 7.4 nC = 7.4 * 10 ^ -9 C); x – distance between round plates (x = 4 mm = 4 * 10 ^ -3 m); ε is the dielectric constant of the interlayer (ε = 5); d – diameter of a round plate (d = 16 cm = 16 * 10 ^ -2 m).
Let’s calculate: U = 4q * x / (ε0 * ε * Π * d ^ 2) = 4 * 7.4 * 10 ^ -9 * 4 * 10 ^ -3 / (8.85 * 10 ^ -12 * 5 * 3.14 * (16 * 10 ^ -2) ^ 2) = 33.29 V.
Answer: The voltage across the indicated capacitor is 33.29 V.