Each of a parallel-plate air capacitor has an area S. What amount of work has to be performed to slowly increase the distance between the plates from x1 to x2. If the voltage across the capacitor, which is equal to V, is kept constant in the process. [This question is only for Dropper and XII batch]

1. ε0SV2

2. ε0SV21x1-1x2

3. ε0SV221x1-1x2

4. ε0SV

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Using the concept of energy density, find the total energy stored by a shell of radius R and charge Q. [This question is only for Dropper and XII batch]

1. Q2πε0R

2. Q22πε0R

3. Q24πε0R

4. Q28πε0R

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The electric field vector in a region given by E=(3i^+4yj^)Vm-1. Calculate the potential at (1m, 1m) taking potential at origin to be zero. [This question is only for Dropper and XII batch]

1. 5V

2. 3V

3. -1V

4. -5V

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A ball of radius R carries a positive charge throughout its volume, such that the volume density of charge depends on distance r from the ball's centre as ρ=ρ01-rR, where ρ0 is a constant. Assuming the permittivity of ball to be one, find magnitude of electric field as a function of distance r, both inside  the ball. [This question is only for Dropper and XII batch]

1.ρ0r3ε0

2. ρ0(4rR-3r2)12ε0R 

3. ρ0(4rR-3r2)3ε0R

4. ρ0(4rR-5r2)3ε0R

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Find electric field due to a uniformly charged, long and thin rod

[This question is only for Dropper and XII batch]

1. kλr

2. kλ2r

3. 2kλr

4. kλ4r

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Find electric field at the centre of arc which subtends 'θ' angle at centre

[This question is only for Dropper and XII batch]

1. 2kλrsin θ

2. 2kλrsinθ4

3. 2kλrsinθ2

4. 2kλrsin2θ

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Calculate the electric field on the axis of a very long uniformly charged, thin rod at a distance r from one end. The charge per unit length of the rod is λ[This question is only for Dropper and XII batch]

1. 2kλr

2. kλr

3. kλ2r

4. kλ4r

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Electric field is given by E =100x2 . Find the potential difference between x= 10 and x= 20 m. [This question is only for Dropper and XII batch]

1. 5 V

2. 10 V

3. 15 V

4. 20 V

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The temperature of n moles of an ideal gas is increased from T0 to 2T0 through a process P=αT . Find the work done by the gas. [This question is only for Dropper and XII batch]

1. nRT02

2. nRT0

3. 32nRT0

4. 2 nRT0

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An isolated container at 127°C contains an ice cube of mass 100 g at 0°C. The specific heat C of container varies with temperature according to relation C= a+bT, where a= 0.1 kcal/kg-K and b= 40 m cal/kg K. Find the mass of container, if the final temperature of container is 300 K.
[Take LF= 80 cal/g and specific heat of water 1 cal/g K]

[This question is only for Dropper and XII batch]

1. 500 g

2. 720 g

3. 940 g

4. 1200 g

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