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 Multiple Choice QuestionsMultiple Choice Questions

1.

Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is

  • 1 : 4

  • 4 : 1

  • 1:2

  • 2:1


D.

2:1

straight E subscript straight A over straight E subscript straight B space equals space straight r subscript straight B over straight r subscript straight A space equals space 2 over 1
484 Views

2.

Two point charges + 8q and – 2q are located at x = 0 and x = L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is

  • 2L

  • L/4

  • 8L

  • 4L


A.

2L

fraction numerator straight k 2 straight q over denominator left parenthesis straight x minus straight L right parenthesis squared end fraction plus fraction numerator straight k 8 straight q over denominator straight x squared end fraction space equals space 0 space
rightwards double arrow space straight x space equals 2 straight L
173 Views

3.

A charged ball B hangs from a silk thread S which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

  • cos θ

  • cot θ

  • sin θ

  • tan θ


D.

tan θ

tan space fraction numerator qσ over denominator left parenthesis 2 straight epsilon subscript straight o right parenthesis mg end fraction
367 Views

4.

Charges are placed on the vertices of a square as shown. Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

  • straight E with rightwards arrow on top remains unchanged, V changes 
  • Both straight E with rightwards arrow on top and V change

  • straight E with rightwards arrow on top and V remain unchanged
  • straight E with rightwards arrow on top changes, V remains unchanged

D.

straight E with rightwards arrow on top changes, V remains unchanged
169 Views

5.

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 ≤ r< ∞ , where r is the distance from the centre of the shell? 


A.

167 Views

6.

Which of the following units denotes the dimensions ML2 /Q2, where Q denotes the electric charge?

  • Weber (Wb)

  • Henry (H)

  • Wb/m2

  • H/m2


B.

Henry (H)

182 Views

7.

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields straight E with rightwards arrow on top space and space straight B with rightwards arrow on top, with a velocity straight v with rightwards arrow on top perpendicular to both straight E with rightwards arrow on top space and space straight B with rightwards arrow on top , and comes out without any change in magnitude or direction of straight v with rightwards arrow on top .Then

  • straight v with rightwards arrow on top space equals space straight E with rightwards arrow on top space straight x space straight B with rightwards arrow on top space divided by straight B squared
  • straight v with rightwards arrow on top space equals space straight B with rightwards arrow on top space straight x space straight E with rightwards arrow on top divided by straight B squared
  • straight v with rightwards arrow on top space equals space straight E with rightwards arrow on top space straight x space straight B with rightwards arrow on top divided by straight E squared
  • straight v with rightwards arrow on top space equals space straight B with rightwards arrow on top space straight x space straight E with rightwards arrow on top divided by straight E squared

A.

straight v with rightwards arrow on top space equals space straight E with rightwards arrow on top space straight x space straight B with rightwards arrow on top space divided by straight B squared
319 Views

8.

Two thin wires rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and –q. The potential difference between the centres of the two rings is 

  • QR divided by 4 πε subscript 0 straight d squared
  • fraction numerator straight Q over denominator 2 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets
  • zero

  • fraction numerator straight Q over denominator 4 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets

B.

fraction numerator straight Q over denominator 2 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets
straight v subscript 1 space equals space kq over straight R minus fraction numerator kq over denominator square root of straight R squared plus straight d squared end root end fraction
straight v subscript 2 space equals space fraction numerator negative kq over denominator straight R end fraction plus fraction numerator kq over denominator square root of straight R squared plus straight d squared end root end fraction
174 Views

9.

A charged particle q is shot towards another charged particle Q which is fixed, with a speed v it approaches Q upto a closest distance r and then returns. If q were given a speed 2v, the closest distances of approach would be

  • r

  • 2r

  • r/2

  • r/4


D.

r/4

By principle of conservation of energy
1 half mv squared space equals space kqQ over straight r space..... space left parenthesis straight i right parenthesis

Finally comma space 1 half space straight m left parenthesis 2 straight v right parenthesis squared space equals space fraction numerator begin display style KqQ end style over denominator straight r squared end fraction space... left parenthesis ii right parenthesis
Equation space left parenthesis straight i right parenthesis divided by left parenthesis ii right parenthesis
1 fourth space equals space fraction numerator straight r apostrophe over denominator straight r end fraction
rightwards double arrow space straight r apostrophe space equals space fraction numerator begin display style straight r end style over denominator 4 end fraction

341 Views

10.

Four charges equal to −Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is

  • negative straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis
  • straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis
  • negative straight Q over 2 space left parenthesis 1 space plus 2 square root of 2 right parenthesis
  • straight Q over 2 space left parenthesis 1 space plus 2 square root of 2 right parenthesis

B.

straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis
413 Views