Two parallel rectangular plates measuring 80 mm by 120 mm are separated by 4 mm of mica and carry an electric charge of 0.48 MC. The Voltage between the plates is 500 V. Calculate:
(a) the electric flux density
(b) the electric field strength and
(c) the capacitance of the capacitor.
Answer (2)
Convert all measurements to standard units.
Calculate the area of the plates: A = 0.0096 m 2 .
Calculate the electric flux density: D = A Q = 50000000 C / m 2 .
Calculate the electric field strength: E = d V = 125000 V / m , and the capacitance: C = V Q = 960 F .
The electric flux density is 50000000 C / m 2 , the electric field strength is 125000 V / m , and the capacitance is 960 F .
Explanation
Problem Analysis We are given two parallel rectangular plates with dimensions 80 mm by 120 mm, separated by 4 mm of mica. The plates carry an electric charge of 0.48 MC, and the voltage between them is 500 V. We need to calculate (a) the electric flux density, (b) the electric field strength, and (c) the capacitance of the capacitor.
Unit Conversion First, we need to convert all measurements to standard units (meters and Coulombs).
Plate Dimensions and Given Values The length of the plates is l = 80 mm = 80 × 1 0 − 3 m = 0.08 m .
The width of the plates is w = 120 mm = 120 × 1 0 − 3 m = 0.12 m .
The separation distance is d = 4 mm = 4 × 1 0 − 3 m = 0.004 m .
The electric charge is Q = 0.48 MC = 0.48 × 1 0 6 C = 480000 C .
The voltage between the plates is V = 500 V .
Calculating Electric Flux Density (a) To calculate the electric flux density D , we first need to find the area A of the plates: A = l × w = 0.08 m × 0.12 m = 0.0096 m 2
Then, the electric flux density is given by: D = A Q = 0.0096 m 2 480000 C = 50000000 C / m 2
Calculating Electric Field Strength (b) To calculate the electric field strength E , we use the formula: E = d V = 0.004 m 500 V = 125000 V / m
Calculating Capacitance (c) To calculate the capacitance C of the capacitor, we use the formula: C = V Q = 500 V 480000 C = 960 F
Final Answer Therefore, the electric flux density is 50000000 C / m 2 , the electric field strength is 125000 V / m , and the capacitance is 960 F .
Examples
Understanding capacitors is crucial in designing electronic circuits. For instance, in a camera flash, a capacitor stores energy and releases it quickly to create a bright flash. The calculations we performed help determine the capacitor's ability to store charge (capacitance), the strength of the electric field it generates, and how much charge it can hold per unit area. These parameters are essential for optimizing the flash's brightness and duration, ensuring a well-lit photograph.
The electric flux density between the plates is 50000000 C/m², the electric field strength is 125000 V/m, and the capacitance of the capacitor is 960 F.
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