he 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) When the dielectric is inserted, the electric field (E-field) remains the same because the voltage is kept constant. The E-field is given by E = V/d, where V is the voltage and d is the distance between the plates. So, E = 50V/d.

The displacement field (D-field) is given by D = εE, where ε is the permittivity of the dielectric. The permittivity of the dielectric is given by ε = ε0εr, where ε0 is the permittivity of free space and εr is the relative permittivity. So, D = ε0εrE = ε03.450V/d.

The polarization field (P-field) is given by P = ε0(εr - 1)E = ε0(3.4 - 1)*50V/d.

(b) When the dielectric is inserted with the capacitor disconnected, the charge on the capacitor remains constant. This means that the D-field remains constant. The D-field is given by D = Q/A, where Q is the charge and A is the area of the plates.

The E-field is given by E = D/ε, so E = Q/(Aε03.4).

The P-field is given by P = D - ε0E = Q/A - Q/(A*3.4).

The new voltage between the plates is given by V = Ed = Qd/(Aε03.4).

(a) When the dielectric is inserted, the electric field (E-field) remains the same because the voltage is kept constant. The E-field is given by E = V/d, where V is the voltage (50 V) and d is the distance between the plates.

The displacement field (D-field) is given by D = εE, where ε is the permittivity of the dielectric. The permittivity of the dielectric is given by ε = ε0εr, where ε0 is the permittivity of free space (8.85 x 10^-12 F/m) and εr is the relative permittivity (3.4).

The polarization field (P-field) is given by P = ε0(εr - 1)E.

(b) When the dielectric is inserted with the capacitor disconnected, the charge on the capacitor remains constant. This means that the D-field remains constant. The D-field is given by D = Q/A, where Q is the charge and A is the area of the plates.

The E-field is given by E = D/ε, where ε is the permittivity of the dielectric.

The P-field is given by P = D - ε0E.

The new voltage between the plates is given by V = Ed, where E is the new electric field and d is the distance between the plates.