Title 01. ELECTRIC CHARGES AND FIELDS (1).pdf ✅

ELECTRIC CHARGES AND FIELDS 1.5 Coulomb's Law 1. Two point charges A and B, having charges +Q and −Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes (a) 4F 3 (b) F (c) 9F 16 (d) 16F 9 (2019) 2. Suppose the charge of a proton and an electron differ slightly. One of them is −e, the other is (e + Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given: mass of hydrogen mh = 1.67 × 10−27 kg ] (a) 10−23C (b) 10−37C (c) 10−47C (d) 10−20C (2017) 3. Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d(d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as (a) v ∝ x −1/2 (b) v ∝ x −1 (c) v ∝ x 1/2 (d) v ∝ x (NEET-I 2016) 4. 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 (a) ( 2r √3 ) (b) ( 2r 3 ) (c) ( 1 √2 ) 2 (d) ( r √2 3 ) (2013) 5. 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 ( e being the charge on an electron) (a) 4πε0Fd 2 e 2 (b) √ 4πε0Fe 2 d2 (c) √ 4πε0Fd2 e 2 (d) 4πε0Fd 2 q2 (2010) 6. 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) 1.6 Forces between Multiple Charges 7. 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 q is equal to (a) −Q/4
(b) Q/4 (c) −Q/2 (d) Q/2 (Karnataka NEET 2013, 1995) 8. Point charges +4q, −q and +4q are kept on the X-axis at point x = 0, x = a and x = 2a respectively. Then (a) only −q is in stable equilibrium (b) all the charges are in stable equilibrium (c) all of the charges are in unstable equilibrium (d) none of the charges is in equilibrium. (1988) 1.7 Electric Field 9. An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is (a) smaller (b) 5 times greater (c) 10 times greater (d) equal (2018) 10. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E⃗ . Due to the force qE⃗ , its velocity increases from 0 to 6 m s −1 in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively (a) 2 m s −1 , 4 m s −1 (b) 1 m s −1 , 3 m s −1 (c) 1 m s −1 , 3.5 m s −1 (d) 1.5 m s −1 , 3 m s −1 (2018) 11. 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 2y (c) qEy 2 (d) q 2Ey (1998) 1.8 Electric Field Lines 12. The given figure gives electric lines of force due to two charges q1 and q2. What are the signs of the two charges? (a) q1 is positive but q2 is negative. (b) q1 is negative but q2 is positive. (c) both are negative. (d) both are positive. (1994) 1.9 Electric Flux 13. 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 θ with the horizontal side of the square as shown in figure. The electric flux linked to the surface, in units of volt m is (a) EL 2 (b) EL 2 cos θ (c) EL 2 sin θ (d) zero (2010) 14. A square surface of side L metres is in the plane of the paper. A uniform electric field E⃗ (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) EL 2 (b) EL 2 /2ε0 (c) EL 2 /2 (d) zero (2006) 1.10 Electric Dipole 15. An electric dipole is placed as shown in the figure. The electric potential (in 102 V ) at point P due to the dipole is (ε0 = permittivity of free space and 1 4πε0 = K ) (a) ( 8 5 ) qK (b) ( 8 3 ) qK (c) ( 3 8 ) qK (d) ( 5 8 ) qK (2023) 16. Two point charges −q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R(R >> L) varies as (a) 1 R2 (b) 1 R3 (c) 1 R4 (d) 1 R6 (2022) 17. Polar molecular are the molecules (a) having a permanent electric dipole moment. (b) having zero dipole moment. (c) acquire a dipole moment only in the presence of electric field due to displacement of charges. (d) acquire a dipole moment only when magnetic field is absent. (2021) 18. 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 (a) √2qa along the line joining points (x = 0, y = 0, z = 0 ) and ( x = a, y = a, z = 0 ) (b) qa along the line joining points (x = 0, y = 0, z = 0) and ( x = a, y = a, z = 0 ) (c) √2qa along +x direction (d) √2qa along +y direction. (2007) 19. 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 (a) p 2 and r −3 (b) p and r −2 (c) p −1 and r −2 (d) p and r −3 (1998) 1.11 Dipole in a Uniform External Field 20. An electric dipole is placed at an angle of 30∘ with an electric field of intensity 2 × 105 NC −1 . It experiences a torque equal to 4 Nm . Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm . (a) 4 mC (b) 2 mC (c) 8 mC (d) 6 mC (2023) 21. An electric dipole is placed at an angle of 30∘ with an electric field intensity 2 × 105 NC −1 . It experiences a torque equal to 4 Nm . The charge on the dipole, if the dipole length is 2 cm , is
(a) 8 mC (b) 2 mC (c) 5 mC (d) 7μC (NEET-II 2016) 22. A dipole of dipole moment p is placed in uniform electric field E⃗ , then torque acting on it is given by (a) τ = p ⋅ E⃗ (b) τ = p × E⃗ (c) τ = p + E⃗ (d) τ = p − E⃗ (2001) 1.12 Continuous Charge Distribution 23. A spherical conductor of radius 10 cm has a charge of 3.2 × 10−7C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere? ( 1 4πε0 = 9 × 109 N m2 / C 2 ) (a) 1.28 × 104 N/C (b) 1.28 × 105 N/C (c) 1.28 × 106 N/C (d) 1.28 × 107 N/C (2020) 24. A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the 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 (2008) 25. Electric field at centre O of semicircle of radius a having linear charge density λ given as (a) 2λ ε0a (b) λπ ε0a (c) λ 2πε0a (d) λ πε0a (2000) 1.13 Gauss's Law 26. If ∮ E⃗ ⋅ dS = 0 over a surface, then (a) all the charges must necessarily be inside the surface (b) the electric field inside the surface is necessarily uniform (c) the number of flux lines entering the surface must be equal to the number of flux lines leaving it. (d) the magnitude of electric field on the surface is constant. (2023) 27. What is the flux through a cube of side a if a point charge of q is at one of its corner? (a) 2q ε0 (b) q 8ε0 (c) q ε0 (d) q 2ε0 6a 2 (2012) 28. 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 (2011)