JEE Advanced 2014 · Paper 1 · Physics Q4

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PhysicsMultiple correct+3Question 4 of 60

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C_1$ . When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$ . The electric field in the dielectric is $E_1$ and that in the other portion is $E_2$ . Choose the correct option/options, ignoring edge effects.

Two vertical parallel plates; the top third of the gap is filled with a dielectric (dotted, field E₁, charge Q₁ on that part of the plate) and the lower two thirds is empty (field E₂, charge Q₂).

\dfrac{E_1}{E_2}=1

\dfrac{E_1}{E_2}=\dfrac1K

\dfrac{Q_1}{Q_2}=\dfrac3K

\dfrac C{C_1}=\dfrac{2+K}K

Answer and worked solution

Official answer: A, D

Two capacitors in parallel. Both portions share the plate separation $d$ and the potential difference $V$ .

(A)/(B) $E=V/d$ in both portions, so $E_1/E_2=1$ . (A) true, (B) false.
(C) $C_1=\dfrac{K\varepsilon_0A}{3d}$ , $C_2=\dfrac{2\varepsilon_0A}{3d}$ , so $\dfrac{Q_1}{Q_2}=\dfrac{C_1}{C_2}=\dfrac K2$ . False.
(D) $C=C_1+C_2=\dfrac{(K+2)\varepsilon_0A}{3d}$ , so $\dfrac C{C_1}=\dfrac{2+K}K$ . True.

(A), (D)

Topics:Dielectrics Series and parallel combinations

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JEE Advanced 2014 · Paper 1, Physics question 4