Identify the incorrect statement(s) among the following:
When a dielectric medium is introduced between the plates of a charged capacitor the electric field inside the dielectric changes due to polarisation. \( E_0 \) is the electric field between the plates of capacitor without dielectric and \( E_p \) is the electric field due to polarisation.
(A) If a plate of dielectric constant k, thickness t is placed between the plates of a charged capacitor of area A of the plate and having distance d between the plates, then the new capacitance will be \( A\varepsilon_0/(d - t(1 + 1/k)) \)
(B) The electric field between plates of the charged capacitor when the dielectric is introduced will be \( E = (E_0 - E_p) \)
(C) Dielectric constant of the dielectric placed between plates of charged capacitor will be \( k = E_0/(E_0 - E_p) \)
(D) Dielectric strength of the dielectric is the maximum value of the electric field which may be applied before its break down.
Choose the correct answer from the option given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) only
(A) If a plate of dielectric constant k, thickness t is placed between the plates of a charged capacitor of area A of the plate and having distance d between the plates, then the new capacitance will be \( A\varepsilon_0/(d - t(1 + 1/k)) \). — False statement. With the slab, the field is \( E_0 \) in the air gap of width \( d - t \) and \( E_0/k \) inside the slab, so the potential difference is
\( \displaystyle V = E_0 (d - t) + \frac{E_0}{k}\,t = E_0\left[d - t\left(1 - \frac{1}{k}\right)\right] \)
\( \displaystyle C = \frac{Q}{V} = \frac{\varepsilon_0 A}{d - t\left(1 - \frac{1}{k}\right)} \)
The correct factor is \( 1 - 1/k \), not \( 1 + 1/k \).
(B) The electric field between plates of the charged capacitor when the dielectric is introduced will be \( E = (E_0 - E_p) \). — True statement. The polarisation charges on the faces of the dielectric produce a field \( E_p \) opposite to \( E_0 \), so the net field is reduced.
(C) Dielectric constant of the dielectric placed between plates of charged capacitor will be \( k = E_0/(E_0 - E_p) \). — True statement. The net field is \( E = E_0/k \), so \( k = E_0/E = E_0/(E_0 - E_p) \).
(D) Dielectric strength of the dielectric is the maximum value of the electric field which may be applied before its break down. — True statement. This is the definition of dielectric strength.
Only (A) is incorrect, which is Option (1).