JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Capacitance

WhatsApp Email

q_{f}

is the free charge on the capacitor plates and

q_{b}

is the bound charge on the dielectric slab of dielectric constant

k

placed between the capacitor plates, then bound charge

q_{b}

can be expressed as :

(A) $q_{b} = q_{f} (1 + \frac{1}{k})$
(B) $q_{b} = q_{f} (1 - \frac{1}{k})$
(C) $q_{b} = q_{f} (1 - \frac{1}{k})$ ✓ Correct
(D) $q_{b} = q_{f} (1 + \frac{1}{k})$

Answer: (C)

Solution

The net electric field inside the dielectric is

E_{net} = \frac{E _{0}}{k}

, where

E_{0}

is the field due to free charges. The field due to bound charges is

E_{b} = E_{0} - E_{net} = E_{0} (1 - \frac{1}{k})

. Since field is proportional to charge,

q_{b} = q_{f} (1 - \frac{1}{k})

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Capacitance →

More JEE Main questions on Capacitance

A capacitor $P$ with capacitance $10 \times 1 0^{- 6} F$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20 \times 1 0^{- 6} F$ . The char …
JEE Main 2026View solution →
The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_{1} = 2, K_{2} = 3$ , and $K_{3} = 5$ (as shown in the figure). If new capacitance is …
JEE Main 2026View solution →
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25%$ more charge from the battery. The dielectric con …
JEE Main 2026View solution →
Three parallel plate capacitors each with area A and separation d are filled with two dielectric (k₁ and k₂) in the following fashion. Which of the following is true? (k₁ > k₂)
JEE Main 2026View solution →
Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of c …
JEE Main 2026View solution →
A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates.
A sheet having thickness $(\frac{1}{3})^{rd}$ of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitan …
JEE Main 2026View solution →