A positively charged particle moving along x-axis with a

Question

Q.1 Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is

(a) F/4       (b)3F/4         (c)F/8           (d)3F/8

Q.2 The intensity of the electric field required to keep a water drop of radius 10^-5cm just suspended in air when charged with one electron is approximately (g = 10newton/kg, e = 1.6 x 10^-19 coulomb)

(a)260 volt/cm (b) 260 newton/coulomb (c) 130 volt/cm (d) 130 newton/coulomb

Q.3 Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side a. The magnitude of electric field at the point C is

(a) q/4Πε₀a²                (b)√2q/4Πε₀a²
(c)√3q/4Πε₀a²             (d) q/2Πε₀a²

Q.4 The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

(a) E_A > E_B > E_C (b) E_A = E_B - E_C (c) E_A = E_C > E_B (d) E_A = E_C > E_B

Q.5 Three identical point charges, as shown are placed at the vertices of an isosceles right angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point M of the hypotenuse

(a) 1 (b) 2
(c) 3 (d) 4

Q.6 Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero

Q.7 A positively charged particle moving along x-axis with a certain velocity enters a uniform electric field directed along positive y-axis. Its
(a) Vertical velocity changes but horizontal velocity remains constant
(b) Horizontal velocity changes but vertical velocity remains constant
(c) Both vertical and horizontal velocities change
(d) Neither vertical nor horizontal velocity changes

Q.8 An electric dipole is placed along the x- axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle Π/3 with the x-axis. If the electric field at makes an angle with the x-axis, the value of θ would be

(a) Π/3 (b) Π/3 + tan^-1(√3/2) (c) 2Π/3 (d) tan^-1(√3/2)

Q.9 Electric charges q, q, -2q are placed at the corners of an equilateral triangle ABC of side l. The magnitude of electric dipole moment of the system is

(a) ql (b) 2ql (c)√3ql  (d)4ql

Q.10 The electric field at a point on equatorial line of a dipole and direction of the dipole moment

(a) Will be parallel (b) Will be in opposite direction
(c) Will be perpendicular (d) Are not related

Q.11 The electric intensity due to a dipole of length 10 cm and having a charge of 500μC, at a point on the axis at a distance 20 cm from one of the charges in air, is

(a) 6.25 x 10⁷ N/C (b) 9.28 x 10⁷ N/C (c) 13.1 x 11¹¹ N/C (d) 20.5 x 10⁷ N/C

Q.12 The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the dipole is rotated through an angle of 90° about its perpendicular axis, the electric field at the same point will be

(a) E (b) E/4 (c) E/2 (d) 2E

Q.13 Charge q is uniformly distributed over a thin half ring of radius R. The electric field at the centre of the ring is

(a) q/2Πε₀R²                (b)q/4Πε₀R²
(c) q/4Πε₀R²                (d) q/2Πε₀R²

Q.14 There is a uniform electric field of strength 10³ V/m along y-axis. A body of mass 1g and charge 10^-6C is projected into the field from origin along the positive x-axis with a velocity 10m/s. Its speed in m/s after 10s is (Neglect gravitation)

(a) 10         (b) 5√2                    (c)10√2        (d) 20

Q.15 Three charges and are placed as shown in the figure. The x-component of the force on is proportional to
(a)q₂/b² - q₃/a² sinθ        (b)q₂/b² - q₃/a² sinθ
(c)q₂/b² - q3/a² sinθ        (d) q₂/b² - q₃/a² sinθ