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 Multiple Choice QuestionsMultiple Choice Questions

11.

Two parallel large thin metal sheets have equal surface charge densities ( σ = 26.4 × 10-12 C/m2 ) of opposite signs. The electric field between these sheets is

  • 1.5 N/C

  • 1.5 × 10-10 N/C

  • 3 N/C

  • 3 × 10-10 N/C 


C.

3 N/C

Electric field  between the sheets is

      E =  σε0

          = 26.4 × 10-128.85 × 10-12

Since given:- ε0 = 8.85 × 10-12 C2 / (Nm2)

       E  ≈ 3 N/C


12.

The figure shows three points A, B and C in a region of a uniform electric field E. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good?

 

  • VA = VB = VC

  • VA = VB > VC

  • VA = VB < VC

  • VA > VB = VC


B.

VA = VB > VC

Electric lines of force flow from higher potential to lower potential so,

VA = VB > VC


13.

If an insulated non-conducting sphere of radius R has charge density ρ. The electric field at a distance r from the centre of sphere (r > R) will be

  • ρ R3εo

  • ρ rεo

  • ρ r3 εo

  • 3 ρ Rεo


C.

ρ r3 εo

Gauss law allows us to determine the electric field at a point when there is sufficient symmetry.

Charge which is enclosed in the surface is given by

σ = 43 π r3ρNow according ro Gaussian lawε ϕ E ds =σεo E 4π r2=43π r3ρE = ρ r3 εo


14.

Number of extra electrons in a body of charge -80μC, is

  • 80 × 1015

  • 80 × 10−15

  • 5 × 1014

  • 1.28 × 10−17


C.

5 × 1014

Charge on an electron = 1.6 × 10−19 C

Number of extra electrons in an object having charge −80μC

                                = 80 × 10-61.6 × 10 -19

                                = 5 × 1014


15.

Two spheres of radii R1 and R2 respectively are charged and joined by a wire. The ratio of the electric field of spheres is :

  • R22R12

  • R12R22

  • R2R1

  • R1R2


C.

R2R1

The spheres are joined by the wire, so their potential will become equal.

V1 = V2

14πε0q1R1 = 14πε0q2R2

 q1q2 = R1R2

E1E2 = kq1R12kq2R22

= q1q2R2R12= R1R2R2R12

= R2/R1


16.

A conducting sphere of radius R = 20 cm is given by a charge Q = 16μC. What is E at centre?

  • 3.6×106 N/C

  • 1.8×10N/C

  • Zero

  • 0.9×106 N/C


C.

Zero

The value of E at the centre of the sphere is zero. Since the centre of the sphere is placed within the Gaussian surface. The use of Gauss law to examine the electric field of a charged sphere shows the electric field enviornment outside the sphere is identical to that of point charge. 

Therefore the potential is the same as that of a point charge

V = Q4πε0r

hence E=0


17.

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

  • 4πq6 4πε0

  • πq64πε0

  • q64πε0

  • 2πq64πε0


A.

4πq6 4πε0

According to Gauss's theorem, electric flux through the cube (closed surface),

                ϕ = qε0

Since, cube has six surfaces and all the faces are symmetrical, therefore electric flux through any face

              ϕ' = q6ε0 = 4πq64πε0


18.

Two charged spheres separated by a distance d exert some force (F) on each other. If they are immersed in a liquid of dielectric constant 4, then what is the force exerted, if all other conditions are same ?

  • 2F

  • 4F

  • F2

  • F4


D.

F4

     Fi = 14πε0q1q2d2      ..... (i)    Ff = 14πε0k q1q2d2or Ff = 14 14πε0q1q2d2  = 14F         [from eqn (i)]


19.

The spatial distribution of the electric field due to two charges (A, B) is shown in figure. Which one of the following statements is correct?

  • A is +ve and +B is -ve and A > B

  • A is -ve and B is +ve; A = B

  • both are +ve but A > B

  • both are -ve but A > B


A.

A is +ve and +B is -ve and A > B

The lines proceed from the positive and lines will reach B, if B is negative.

The number of lines/unit area i.e the intensity of lines is great the charge.

A is positive, B is negative and  A > B


20.

In a discharge tube ionization of enclosed gas is produced due to collisions between

  • positive ions and neutral atoms/molecules

  • negative electrons and neutral atoms/molecules

  • photons and neutral atoms/molecules

  • neutral gas atoms/molecules


B.

negative electrons and neutral atoms/molecules

In a discharge tube, after being accelerated though a high potential difference the ions in the gas strike the cathode with huge kinetic energy. This collision liberates electrons from the cathode. These free electrons can further liberate ions from gas molecules through collisions. The positive ions are attracted towards the cathode and negatively electrons move towards anode. Thus, ionization of gas results.

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