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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 C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.


(A)𝐸𝐸1𝐸𝐸2=1
(B)𝐸𝐸1𝐸𝐸2=1𝐾𝐾
(C)𝑄𝑄1𝑄𝑄2=3𝐾𝐾
(D)𝐶𝐶𝐶𝐶1=2+

Let𝐸𝐸1(𝑟&#119903, 𝐸𝐸2(𝑟&#119903 and 𝐸𝐸3(𝑟&#119903 be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density σ. If 𝐸𝐸1(𝑟𝑟0)=𝐸𝐸2(𝑟𝑟0)=𝐸𝐸3(𝑟𝑟0) at a given distance r0, then
(A)𝑄𝑄=4𝜎𝜎𝜎𝜋𝜋𝑟𝑟02
(B)𝑟𝑟0= 𝜆𝜆2𝜋𝜋𝜋𝜎𝜎
(C) 𝐸𝐸1(𝑟𝑟02⁄)= 2𝐸𝐸2(𝑟𝑟02⁄)
(D)𝐸𝐸2(𝑟𝑟02⁄)=4𝐸𝐸3(𝑟𝑟02⁄)

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d.The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?

(A) 4 if wires are in parallel
(B) 2 if wires are in series
(C)1 if wires are in series
(D) 0.5 if wires are in parallel




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