MHT CET · Physics · Capacitance
The dielectric slab is introduced between the plates of a parallel plate charged capacitor. Which one of the following quantities will not change?
- A The charge on the capacitor.
- B The potential difference between the plates.
- C The energy stored in the capacitor.
- D The electric field between the plates of a capacitor.
Answer & Solution
Correct Answer
(A) The charge on the capacitor.
Step-by-step Solution
Detailed explanation
Only the amount of charge stored in the capacitor will remain constant when the dielectric is inserted between the plates (isolated system).
Charge will redistribute, such on the plate \(Q\left(1-\frac{1}{K}\right)\) and \(\frac{Q}{K}\) on the dielectric interface.
The electric field present between the plates of capacitor changes because it varies with the dielectric constant:
\(E^{\prime}=\frac{Q}{4 \pi \varepsilon_0 K}=\frac{E}{K}\)
The capacitance increases as:
\(C^{\prime}=\frac{K \varepsilon_0 A}{d}=K C\)
The dielectric constant also affects the potential difference as:
\(\begin{aligned} & Q=C^{\prime} V^{\prime}=C K V^{\prime}=C V \\ & \therefore V^{\prime}=\frac{V}{K}\end{aligned}\)
and the energy stored in the capacitor:
\(U^{\prime}=\frac{1}{2} \frac{Q^2}{C^{\prime}}=\frac{U}{K}\)
Charge will redistribute, such on the plate \(Q\left(1-\frac{1}{K}\right)\) and \(\frac{Q}{K}\) on the dielectric interface.
The electric field present between the plates of capacitor changes because it varies with the dielectric constant:
\(E^{\prime}=\frac{Q}{4 \pi \varepsilon_0 K}=\frac{E}{K}\)
The capacitance increases as:
\(C^{\prime}=\frac{K \varepsilon_0 A}{d}=K C\)
The dielectric constant also affects the potential difference as:
\(\begin{aligned} & Q=C^{\prime} V^{\prime}=C K V^{\prime}=C V \\ & \therefore V^{\prime}=\frac{V}{K}\end{aligned}\)
and the energy stored in the capacitor:
\(U^{\prime}=\frac{1}{2} \frac{Q^2}{C^{\prime}}=\frac{U}{K}\)
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