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Section A, , //X, , •, , Write the answer of the following questions. [Each carries 2 Marks], , 1., , Derive an expression for the electric potential in a electric field of positive point charge at distance r., , 2., , Write an equation of potential due to an electric dipole and give its important features. Discuss, its special cases., , [32], , 3. ) (a) Calculate the potential at a point P due to a charge of 4 ´ 10–7 C located 9 cm away., , (b) Hence obtain the work done in bringing a charge of 2 ´ 10–9 C from infinity to the point P., Does the answer depend on the path along which the charge is brought ?, 4. ) Two charges 3 ´ 10–8 C and – 2 ´ 10–8 C are located 15 cm apart. At what point on the line joining, the two charges is the electric potential zero ? Take the potential at infinity to be zero., 5. ) (a) Determine the electrostatic potential energy of a system consisting of two charges 7 mC and, – 2 mC (and with no external field) placed at (– 9 cm, 0, 0) and (9 cm, 0, 0) respectively., , SIR, , (b) How much work is required to separate the two charges infinitely away from each other ?, (c) Suppose that the same system of charge is now placed in an external electric field, E = A(1/r2); A = 9 ´ 105 NC–1 m2 . What would the electrostatic energy of the configuration be ?, , AZ, AZ, , 6.6) A molecule of a substance has a permanent electric dipole moment of magnitude 10 –29 C m. A mole of, this substance is polarised (at low temperature) by applying a strong electrostatic field of magnitude, 106 V m–1. The direction of the field is suddenly changed by an angle of 60º. Estimate the heat released, by the substance in aligning its dipoles along the new direction of the field. For simplicity, assume, 100 % polarisation of the sample. 1 mole = 6 ´ 1023 molecules, , 2.1), Two charges 5 ´ 10–8 C and – 3 ´ 10–8 C are located 16 cm apart. At what point(s) on the line, 7., joining the two charges is the electric potential zero ? Take the potential at infinity to be zero., 2.2), A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential, 8., at the centre of the hexagon., 2.4), A spherical conductor of radius 12 cm has a charge of 1.6 ´ 10–7 C distributed uniformly on its, 9., surface. What is the electric field, (a) inside the sphere., , (b) just outside the sphere., , (c) at a point 18 cm from the centre of the sphere ?, 2.5) A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1 pF = 10–12 F)., 10., What will be the capacitance if the distance between the plates is reduced by half and the space, between them is filled with a substance of dielectric constant 6 ?, ), Three, capacitors each of capacitance 9 pF are connected in series., 11., (a) What is the total capacitance of the combination ?, (b) What is the potential difference across each capacitor if the combination is connected to a, 120 V supply ?, 12. ) Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel., , (a) What is the total capacitance of the combination ?, (b) Determine the charge on each capacitor if the combination is connected to a 100 V supply., 13. ) In a parallel plate capacitor with air between the plates each plate has an area of 6 ´ 10–3 m2 and, the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor, is connected to a 100 V supply, what is the charge on each plate of the capacitor ?, , 2.9) Explain what would happen if in the capacitor given in exercise 2.8 a 3 mm thick mica sheet (of, 14., dielectric constant = 6) were inserted between the plates,, (a) while the voltage supply remained connected.
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2.9) Explain what would happen if in the capacitor given in exercise 2.8 a 3 mm thick mica sheet (of, dielectric constant = 6) were inserted between the plates,, (a) while the voltage supply remained connected., (b) after the supply was disconnected., 15.10) A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor ?, 16.11) A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected, to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process ?, Section B, , //X, , •, , Write the answer of the following questions. [Each carries 4 Marks], , 17., , Derive the formula for the electric potential due to an electric dipole at a point from it., , 18., , What is parallel plate capacitor ? Obtain the formula for the capacitance of such a parallel plate, capacitor and on which factors does the value of capacitance depend ?, , 19., , What is a series connection of capacitors ? Obtain the formula for the effective capacitance in, , [40], , the series combination of two different capacitors., 20., , Obtain the formula for the effective capacitance of the series combination of different n capacitors., , 21., , What is a parallel connection of capacitors ? Obtain the formula for the effective capacitance in, the parallel combination of two different capacitors., How does a capacitor store energy ? And obtain the formula for the energy stored in the capacitor ?, , 23., , Obtain the expression for the energy stored per unit volume in a charged capacitor., , SIR, , 22., , 24. ) A slab of material of dielectrical constant K has the same area as the plates of a parallel-plate, æ 3ö, capacitor but has a thickness ç ÷ d , where d is the separation of the plates. How is the, è 4ø, , capacitance changed when the slab is inserted between the plates ?, , +Q –Q, +, +, +, +, , B, –Q – – – –, +Q ++++, A, , C2, , –, –, –, –, , C1, , AZ, AZ, , 2.9) A network of four 10 mF capacitors is connected to a 500 V supply, as shown in figure. Determine, 25., (a) the equivalent capacitance of the network and (b) the charge on each capacitor. (Note, the, charge on a capacitor is the charge on the plate with higher potential, equal and opposite to the, charge on the plate with lower potential)., C, , C3, +, +, +, +, , C4, , –, –, –, –, , ++++ +Q, – – – – –Q, , D, , +Q –Q, 500 V, , 26. 0) (a) A 900 pF capacitor is charged by 100 V battery (From figure (a)). How much electrostatic, energy is stored by the capacitor ? (b) The capacitor is disconnected from the battery and, connected to another 900 pF capacitor (From figure (b)). What is the electrostatic energy stored, by the system ?, +Q –Q, Q+, +, –, – -Q, +, –, +, –, +, –, +, – 2, 2+, +, –, –, +, –, +, –, +, +, –, –, +, +, –, –, +, +, –, –, C, C, , 100 V, + –, Figure (a), , Q+, +, 2+, +, +, +, +, +, , – -Q, –, – 2, –, –, –, –, –, , C, Figure (b)
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+, +, +, +, , –, –, –, –, , AZ, AZ, , SIR, , C, Figure (b)
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//X, , •, , Section A, Write the answer of the following questions. [Each carries 2 Marks], , 1., , Welcome To Future - Quantum Paper, , [32]
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2., , 3., , Welcome To Future - Quantum Paper
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4., , Welcome To Future - Quantum Paper
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5., , Welcome To Future - Quantum Paper
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6., , Welcome To Future - Quantum Paper
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7., , Welcome To Future - Quantum Paper
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8., , Welcome To Future - Quantum Paper
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9., , 10., , 11., , Welcome To Future - Quantum Paper
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12., , Welcome To Future - Quantum Paper
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13., , 14., , Welcome To Future - Quantum Paper
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15., , 16., , //X, , •, , Section B, Write the answer of the following questions. [Each carries 4 Marks], , 17., , Welcome To Future - Quantum Paper, , [40]
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Welcome To Future - Quantum Paper
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Welcome To Future - Quantum Paper
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18., , Welcome To Future - Quantum Paper
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19., , Welcome To Future - Quantum Paper
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20., , Welcome To Future - Quantum Paper
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21., , 22., , Welcome To Future - Quantum Paper
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23., , Welcome To Future - Quantum Paper
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24., , 25., , Welcome To Future - Quantum Paper
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Welcome To Future - Quantum Paper
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26., , Welcome To Future - Quantum Paper
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Welcome To Future - Quantum Paper
