n air gapped parallel plate capacitor has plate separation 0.01 m.(a) (2 marks) The capacitor is charged to 50 V, and remains connectedto the voltage source so that voltage remains at 50 V as a dielectricwith r = 3.4 is inserted so that it completely fills the gap between theplates. Find the magnitudes of the E-field, D-field, and P-field. Ignoreany possible fringing effects.
Question
n air gapped parallel plate capacitor has plate separation 0.01 m.(a) (2 marks) The capacitor is charged to 50 V, and remains connectedto the voltage source so that voltage remains at 50 V as a dielectricwith r = 3.4 is inserted so that it completely fills the gap between theplates. Find the magnitudes of the E-field, D-field, and P-field. Ignoreany possible fringing effects.
Solution
The electric field (E-field) in a capacitor is given by the equation E = V/d, where V is the voltage and d is the distance between the plates.
Step 1: Calculate the E-field E = V/d = 50V / 0.01m = 5000 V/m
The displacement field (D-field) in a dielectric material is given by the equation D = εr * ε0 * E, where εr is the relative permittivity of the material and ε0 is the permittivity of free space (approximately 8.85 x 10^-12 F/m).
Step 2: Calculate the D-field D = εr * ε0 * E = 3.4 * 8.85 x 10^-12 F/m * 5000 V/m = 1.51 x 10^-7 C/m^2
The polarization field (P-field) in a dielectric material is given by the equation P = ε0 * (εr - 1) * E.
Step 3: Calculate the P-field P = ε0 * (εr - 1) * E = 8.85 x 10^-12 F/m * (3.4 - 1) * 5000 V/m = 1.06 x 10^-7 C/m^2
So, the magnitudes of the E-field, D-field, and P-field are 5000 V/m, 1.51 x 10^-7 C/m^2, and 1.06 x 10^-7 C/m^2, respectively.
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