A parallel plate air-core capacitor of capacitance C is connected across a source of constant potential difference V. When a dielectric plate ( dielectric constant K ) is introduced between the two plates then :

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The electric field intensity between the two plates does not change

Some charge from the capacitor will flow back into the source.

(K-1)CV extra charge flows from the source into the capacitor.

The work done by the external agent in inserting the slab is $- \frac{1}{2} (K - 1) C V^{2}$

answer is B, C, D.

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Detailed Solution

Here potential difference across the capacitor remains constant & C increases to KC . So Q increases to KCV & hence option (2) is correct.

$E = \frac{V}{d}$ as both V & d are constant, so E remain same .So (3) is correct .

$W_{b} = - (K - 1) C V \times V, U_{i} = \frac{1}{2} C V^{2}, U_{f} = \frac{1}{2} K C V^{2}, h e a t d i s s i p a t i o n i s z e r o N o w W_{b} + W_{e} = (U_{f} - U_{i}) + H e a t d i s s i p a t e d . T h e r e f o r e, W_{e} = - \frac{1}{2} (K - 1) C V^{2}$