## NEET AIPMT Physics Chapter Wise Solutions -Electrostatics

NEET AIPMT Physics Chapter Wise SolutionsBiology Chemistry

**1. A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is**

**2. If potential (in volts) in a region is expressed as V(x, y, z) = 6xy – y + 2yz, the electric field (in N/C) at point (1, 1, 0) is**

**3. The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius ‘a’ centred at the origin of the field, will be given by**

**4. A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?**

(a) The change in energy stored is CV^{2} ( -1)

(b) The charge on the capacitor is not conserved.

(c) The potential difference between the plates decreases K times.

(d) The energy stored in the capacitor decreases K times. **(AIPMT 2015, Cancelled)**

**5. Two thin dielectric slabs of dielectric constants K _{1} and K_{2} (K_{1} < K_{2}) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by**

**6. A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are**

**7. In a region , the potential is represented by V(x,y,z)=6x – 8xy – 8y+6yz where V is involts and x,y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is**

(a) 6N

(b) 30 N

(c) 24 N

(d) 4 N** (AlPMT 2014)**

**8. A, B and C are three points in a uniform electric field. The electric potential is**

(a) maximum at C

(b) same at all the three points A, B and C

(c) maximum at A

(d) maximum at B** (NEET 2013)**

**9. Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:**

**10. An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90° is**

(a) p^{2}E

(b) pE

(c) infinity

(d) pE^{2}** ( Karnataka NEET 2013)**

**11. A charge ‘q’ is placed at the centre of the line joining two equal charges ‘Q’ The system of the three charges will be in equilibrium if V is equal to**

(a) -Q/4

(b) Q/4

(c) -Q/2

(d) Q/2 **( Karnataka NEET 2013)**

**12. An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when θ = 90°, the torque and the potential energy of the dipole will respectively be**

(a) pEsinθ, -pEcosθ

(b) pEsinθ, -2pEcosθ

(c) pEsinθ, 2pEcosθ

(d) pEcosθ, -pEsinθ** (Prelims 2012)**

**13. Four point charges -Q, q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is**

**14. What is the flux through a cube of side a if a point charge of q is at one of its comer?**

**15. A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in Ihe capacitor is**

**16. Two metallic spheres of radii 1 cm and 3 cm are are given charges of-1 x 10 ^{-2}C and 5 x 10^{-2} C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is**

(a) 2 x 10

^{-2}C

(b) 3 x 10

^{-2}C

(c) 4 x 10

^{-2}C

(d) 1 x 10

^{-2}C

**(Mains 2012)**

**17. A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the** **outward electric flux will**

(a) increase four times

(b) be reduced to half

(c) remain the same

(d) be doubled **(Prelims 2011)**

**18. Four electric charges +q,+q, -q and -q are placed at the comers of a square of side 2L (see figure). The electric potential at point A, midway between the two charges +q and +q, is**

**19. Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid points of BC and CA. The work D done in taking a charge Q from D to E is**

**20. The electric potential V at any point (x, y, z), all in metres in space is given by V = 4x ^{2} volt. The electric field at the point (1, 0, 2) in volt/meter, is**

(a) 8 along negative X-axis

(b) 8 along positive X-axis

(c) 16 along negative X-axis

(d) 16 along positive X-axis

**(Mains 2011)**

**21. Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be**

**22. A square surface of side L meter in the plane of the paper is placed in a uniform electric field E(volt/m) acting along the same plane at an angle q with thehorizontal side of the square as shown in figure.**

The electric flux linked to the surface, in units of volt m is

(a) EL2

(b) EL1 cos0

(c) EL1 sinG

(d) zero **( Prelims 2010)**

**23. A series combination of n _{1} capacitors, each of value C_{1} is charged by a source of potential difference 4V. When another parallel combination of n_{2} capacitors, each of value C_{2}, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C_{2}, in terms of C_{1} is then**

**24. Two parallel metal plates having charges +Q and -Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will**

(a) become zero

(b) increase

(c) decrease

(d) remain same** (Mains 2010)**

**25. The electric field at a distance from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance from the centre of the sphere is**

(a) zero

(b) E

(c)

(d) **(Mains 2010)**

**26. Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ, – σ and σ respectively. If V _{A}, V_{B} and V_{C} denote the potentials of the three shells, then, for c = a +b, we have**

**27. Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be**

**28. The electric potential at a point (x, y, z) is given by V=-x ^{2}y – xz^{3} + 4**

**The electric field at that point is**

**29. A thin conducting ring of radius R is given a charge +Q. The electric field at the centre c O of the ring due to the charge on the part AKB of the ring is E. The electric field at the D centre due to the charge on the part ACDB of the ring is**

(a) E along KO

(b) 3E along OK

(c) 3E along KO

(d) E along OK** (Prelims 2008)**

**30. The electric potential at a point in free space due to charge Q coulomb is Q x 10 ^{1}^{1} volts. The electric field at that point is**

**31. A hollow cylinder has a charge q coulomb within it. If f is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of V-m will be**

**32. Charges +q and -q are placed at points A and B respectively which are a distance 2Lapart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is**

**33. Three point charges +q, -2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are**

**34. Two condensers, one of capacity C and other other of capacity C/2 are connected to a K-volt battery, as shown in the figure. The work done in charging fully both the condensers is**

**35. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates**

(a) increases

(b) decreases

(c) does not change

(d) becomes zero. **(2006)**

**36. An electric dipole of moment is lying along a uniform electric field . The work done in rotating the dipole by 90° is**

(a) pE

(b) pE

(c) pE/2

(d) 2pE.** (2006)**

**37. A square surface of side L metres is in the plane of the paper. A uniform electric field (volt/m), also in the plane of the paper, is limited only to the lower half of the square surface (see figure). The electric flux in SI units associated with the surface is**

(a) EL2

(b) EL2/2e0

(c) EL1!2

(d) zero. **(2006)**

**38. A network of four capacitors of capacity equal to C _{1}= C, C_{2} = 2 C, C_{3} = 3 C and C_{4} = 4 C are connected to a battery as shown in the figure. The ratio of the charges on C_{2} and C_{4} is**

(a) 4/7

(b) 3/22

(c) 7/4

(d) 22/3.

**39. As per the diagram a point charge +q is placed at the origin O. Work done in taking another point charge -Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is**

**40. Two charges q _{1} and q_{2} are placed 30 cm apart, as shown in the figure. A third charge q_{3 }is moved along the arc of a circle of radius 40cm from C to D. The change in the potential energy of the system is q_{3}/4πε_{0} k, where k**

(a) 8q

_{1}

(b) 6q

_{1}

(c) 8q

_{2}

(d) 6q

_{2}

**(2005)**

**41. A bullet of mass 2 g is having a charge of 2 μC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s ?**

(a) 5 kV

(b) 50 kV

(c) 5 V

(d) 50 V

**42. An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively**

(a)2q. E and minimum

(b) q .E and p .E

(c) zero and minimum

(d) E and maximum **(2004)**

**43. Three capacitors each of capacity 4μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by**

(a) connecting all of them in series

(b) connecting them in parallel

(c) connecting two in series and one in parallel

(d) connecting two in parallel and one in series **(2003)**

**44. A charge q is located at the centre of a cube. The electric flux through any face is**

**45. Identical charges (-q) are placed at each comers of cube of side b then electrostatic potential energy of charge (+q) which is placed at centre of cube will be**

**46. A capacitor of capacity C _{1} charged upto V volt and then connected to an uncharged capacitor of capacity C_{2}. The final potential difference across each will be**

**47. Some charge is being given to a conductor. Then its potential is**

(a) maximum at surface

(b) maximum at centre

(c) remain same throughout the conductor

(d) maximum somewhere between surface and centre. **(2002)**

**48. A dipole of dipole moment is placed in uniform electric field then torque acting on it is given by**

**49. Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by**

**50. A charge QμC is placed at the centre of a cube, the flux coming out from each face will be**

**51. A charge Q is situated at the comer of a cube, the electric flux passed through all the six faces of the cube is**

**52. Electric field at centre O of semicircle of radius a having linear charge density λ given as**

**53. A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is**

(a) U/2

(b) U/4

(c) 4U

(d) 2U. **(2000)**

**54. What is the effective capacitance between points X and Y?**

(a) 12 pF

(b) 18 pF

(c) 24 pF

(d) 6 pF **(1999)**

**55. When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance**

(a) increases K times

(b) remains unchanged

(c) decreases K times

(d) increases K^{-1} times. **(1999)**

**56. In bringing an electron towards another electron, the electrostatic potential energy of the system**

(a) becomes zero

(b) increases

(c) decreases

(d) remains same **(1999)**

**57. A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes**

**58. A hollow insulated conduction sphere is given a positive charge of 10 pC. What will be the electric field at the centre of the sphere if its radius is 2 metres?**

(a) 20 pC m^{-2}

(b) 5 pC m^{-2}

(c) zero

(d) 8 pC m^{-2}**(1998)**

**59. A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is**

(a) qEy

(b) qE^{2}y

(c) qEy^{2}

(d) q^{2}Ey **(1998)**

**60. A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole), then the electric field at Q is proportional to**

**61. A point charge + q is placed at the centre of a cube of side l. The electric flux emerging from the cube is**

**62. The energy stored in a capacitor of capacity C and potential V is given by**

**63. Two metallic spheres of radii 1 cm atid 2 cm are given chatges 10 ^{-2} C and 5 x 10^{-2} C respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is**

**64. There is an electric field E in x-direction. If the work done on moving a charge of 0.2 C through a distance of 2 m along a line making an angle 60° with x-axis is 4 J, then what is the value of E?**

(a) 5 N/C

(b) 20N/C

(c) V3 N/C

(d) 4N/C. **(1995)**

**65. A charge q is placed at the centre of the line joining two exactly equal positive charges Q. The system of three charges will be in equilibrium, if q is equal to**

(a) -Q

(b) Q/2

(c) -Q/4

(d) +Q. **(1995)**

**66. An electric dipole of moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. This is rotated through an angle 0 from the initial position. The potential energy of the electric dipole in the final position is**

(a) – pE cos θ

(b) pE (1 – cos θ)

(c) pE cos θ

(d) pE sinθ. **(1994)**

**67. The given figure gives electric lines of force due to two charges q _{1} and q_{2}. What are the signs of the two charges?**

**68. Charge q _{2}is at the centre of a circular path with radius r. Work done in carrying charge q_{1} once around this equipotential path, would be**

**69. A hollow metallic sphere of radius 10 cm i s charged such that potential of its surface is 80 V. The potential at the centre of the sphere would be**

(a) 80 V

(b) 800 V

(c) zero

(d) 8 V. **(1994)**

**70. Point charges +4q, -q and +4q are kept on the X-axis at point x = 0, x = a and x = 2a respectively.**

(a) only -q is in stable equilibrium

(b) all the charges are in stable equilbrium

(c) all of the charges are in unstable equilibrium

(d) none of the charges is in equilibrium (1988)

### Explanations