An 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.(b) (2 marks) Start again with the capacitor discharged and air gapped.The capacitor is charged to 50 V, but this time the terminals discon-nected, leaving it charged. After the dielectric is inserted, find themagnitudes of the P-field, E-field, and D-field, and the new voltagebetween the plates. Ignore any possible fringing effects.

(a) 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. So, E = 50V / 0.01m = 5000 V/m.

The displacement field (D-field) in a capacitor is given by the equation D = εr * ε0 * E, where εr is the relative permittivity of the dielectric and ε0 is the permittivity of free space (8.85 x 10^-12 F/m). So, D = 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 is given by the equation P = D - ε0 * E. So, P = 1.51 x 10^-7 C/m^2 - 8.85 x 10^-12 F/m * 5000 V/m = 1.06 x 10^-7 C/m^2.

(b) If the capacitor is disconnected before the dielectric is inserted, the charge Q on the capacitor remains constant. The D-field is then given by D = Q/A, where A is the area of one of the plates. Since the problem does not provide the area of the plates, we cannot calculate the exact value of D.

The E-field in the dielectric is given by E = D / (εr * ε0). Again, without the value of Q or A, we cannot calculate the exact value of E.

The P-field is given by P = D - ε0 * E. Without the values of Q or A, we cannot calculate the exact value of P.

The new voltage across the capacitor is given by V = E * d. Without the values of Q or A, we cannot calculate the exact value of V.

(a) The electric field E in a capacitor is given by E = V/d, where V is the voltage and d is the separation between the plates. So, E = 50V / 0.01m = 5000 V/m.

The displacement field D in a dielectric is given by D = εrε0E, where εr is the relative permittivity of the dielectric and ε0 is the permittivity of free space (8.85 x 10^-12 F/m). So, D = 3.4 * 8.85 x 10^-12 F/m * 5000 V/m = 1.51 x 10^-7 C/m^2.

The polarization field P in a dielectric is given by P = D - ε0E. So, P = 1.51 x 10^-7 C/m^2 - 8.85 x 10^-12 F/m * 5000 V/m = 1.06 x 10^-7 C/m^2.

(b) If the capacitor is disconnected from the voltage source before the dielectric is inserted, the charge Q on the capacitor remains constant. The displacement field D is then given by D = Q/A, where A is the area of one of the capacitor plates. Without knowing A, we can't calculate D.

However, we can say that the electric field E in the dielectric is given by E = D / (εrε0), and the polarization field P is given by P = D - ε0E.

The voltage V across the capacitor is given by V = Ed, so the voltage will increase when the dielectric is inserted. Without knowing the charge Q or the area A, we can't calculate the new voltage.