Q1. Two point charges +q1 and +q2 are fixed with a finite distance ‘d’ between them. It is desired to put a third charge q3 in between these two charges on the line joining them so that the charge q3 is in equilibrium . That is :

• (a) Possible only if q3 is positive
• (b) Possible only if q3 is negative
• (c) Possible irrespective of the sign of q3
• (d) Not possible at all

Q2. Five negative electric charges of magnitude e are placed symmetrically on a circle of radius R. The magnitude of the electric field at the center of the circle is

• (a) e/4πεoR2
• (b) 0
• (c) e/4πεoR2 sin /5
• (d) 5e/4πεoR2

Q3. A thin spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81/7 × 105 Vm-1 . When the field is switched off the drop is observed to fall with terminal velocity 2 × 10-3 ms-1 . Given, g = 9.8 m/s2, viscosity of the air = 1.8 × 10-5 Ns/m2 and the density of oil = 900 kg m-3, the magnitude of q is

• (a) 1.6 × 10-19 C
• (b) 3.2 × 10-19 C
• (c) 4.8 × 10-19 C
• (d) 8.0 × 10-19 C

Q4. A charge q is at the center of two concentric spheres. The outward electric flux through the inner sphere is φ while that through the outer sphere is 2φ. The amount of charge contained in the region between the two spheres is

• (a) 2q
• (b) q
• (c) -q
• (d) -2q

Q5. A sphere of radius R and a uniform total Charge Q is centered at origin, total electric flux through a Gaussian sphere of radius R centered at (0,0,d) is

• (a) zero if d > 2R
• (b) Q/εo if d = 0
• (c) Q/o if d = R
• (d) Q/o if d < R

Q6. If the electric flux through a closed surface S is equal to zero, then

• (a) the volume charge density is zero everywhere inside the surface S
• (b) the electric field at every point on S is zero.
• (c) the electric field is zero at every point inside S
• (d) the net charge enclosed by S is zero

Q7. Electric Potential in a particular region of space is V = 5x – 3x²y + 2yz². The magnitude of electric field at point P(m,0,-2m) is

• (a) 5 N/C
• (b) 6 N/C
• (c) 7.08 N/C
• (d) 9.0 N/C

Q8. A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on x-axis at x = +1 cm and C be the point on the y-axis at y = +1 cm. Then the potentials at the points A, B and C Satisfy

• (a) VA < VB
• (b) VA > VB
• (c) VA < VC
• (d) VA > VC

Q9. Electric potential in region is V(r) = Ar3 + B . Charge enclosed by a sphere of radius R is centered at origin is Qo . Charged enclosed by concentric sphere of radius 2R is

• (a) Qo
• (b) 4Qo
• (c) 16Qo
• (d) 32Qo

Q10. A ring of radius R has charge density +λ on one half and -λ on the other half. Its dipole moment is

• (a) 4λR²
• (b) 2λR²
• (c) 3λR²
• (d) λR²

Q11. Two point charges q and -2q lie at x = -a and x = +a respectively. Which of the following statements is/are correct

• (a) There is only one neutral point on x-y plane
• (b) At large distance r>>a E(r)/E(2r) = 4
• (c) Equipotential lines on x-y plane are circles
• (d) Electric flux through y-z plane is 3q/2εo

Q12. Three concentric metallic spherical shells of radii R, 2R, 3R are given charges Q1, Q2, Q3 respectively. It is found that the surface charge densities on the outer surface of the shells are equal. Then, the ratio of the charges given to the shells Q1 : Q2 : Q3 is

• (a) 1 : 2 : 3
• (b) 1 : 3 : 5
• (c) 1 : 4 : 9
• (d) 1 : 8 : 18

Q13. A steady current in a straight conducting wires produces a surface charge on it. Let Eout and Ein be the magnitudes of the electric fields just outside and just inside respectively. Which of the following statements is true for these fields ?

• (a) Eout is always greater than Ein
• (b) Eout is always smaller than Ein
• (c) Eout could be greater or smaller than Ein
• (d) Eout is equal to Ein

Q14. A charge q is placed at the centre of an otherwise neutral dielectric sphere of radius ‘a’ and relative permittivity εr . We denote the expression q/4πεo by E(r). Which of the following statement is false ?

• (a) The electric field inside the sphere, r<a, is given by E(r)
• (b) The field Outside the sphere, r>a, is given by E(r)
• (c) The total charge inside a sphere of radius r>a is given by q.
• (d) The total charge outside a sphere of radius r<a is given by q.

Q15. A bound volume charge density inside the sphere at a distance r from the centre is :

• (a) -4kR
• (b) -4kr
• (c) -4kr²
• (d) -4kr3

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