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.

To solve this problem, we need to understand the relationships between the electric field (E), the displacement field (D), the polarization field (P), and the voltage in a capacitor.

1. The electric field (E) in a capacitor is given by the equation E = V/d, where V is the voltage and d is the distance between the plates. Since the voltage is 50V and the distance is not specified, we'll call it d. So, E = 50/d.

2. The displacement field (D) in a capacitor is given by the equation D = εE, where ε is the permittivity of the dielectric. Without the specific value of ε, we'll just call it ε for now. So, D = εE = ε(50/d).

3. The polarization field (P) in a capacitor is given by the equation P = ε0χE, where ε0 is the permittivity of free space and χ is the electric susceptibility of the dielectric. Without the specific values of ε0 and χ, we'll just call them ε0 and χ for now. So, P = ε0χE = ε0χ(50/d).

4. After the dielectric is inserted, the voltage between the plates will change. The new voltage (V') can be found by the equation V' = ED/ε, where E is the electric field and D is the displacement field. Substituting the previous equations, we get V' = (50/d)(ε(50/d))/ε = 50^2/d^2.

So, the magnitudes of the P-field, E-field, and D-field, and the new voltage between the plates are P = ε0χ(50/d), E = 50/d, D = ε(50/d), and V' = 50^2/d^2, respectively.

To solve this problem, we need to understand the relationship between the electric field (E), the displacement field (D), and the polarization field (P) in a dielectric material.

1. The electric field (E) is given by the voltage (V) divided by the distance (d) between the plates of the capacitor. Since the voltage is 50V and the dielectric is inserted, the electric field remains the same. So, E = V/d.

2. The displacement field (D) in a dielectric is given by the permittivity of free space (ε0) times the electric field (E). So, D = ε0 * E.

3. The polarization field (P) is the displacement field (D) minus the product of the permittivity of free space (ε0) and the electric field (E). So, P = D - ε0 * E.

4. After the dielectric is inserted, the voltage across the capacitor changes. The new voltage (V') is the product of the electric field (E) and the thickness of the dielectric (d'). So, V' = E * d'.

Please note that the exact values of D, P, and V' depend on the specific values of ε0, d, and d', which are not given in the problem.