31. The formation of a dipole is due to two equal and dissimilar point charges placed at a
    

1. 1. short distance

   
   
   

   2. long distance

   
   
   

   3. above each other

   
   
   

   4. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Dipole is formed when two equal and unlike charges are placed at a short distance.

   Correct Option: A

   Dipole is formed when two equal and unlike charges are placed at a short distance.

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32. Intensity of an electric field (E) depends on distance r, due to a dipole, is related as

1. 1. E ∝	1
      	r

      
      

   
   
   

   2. E ∝	1
      	r2

   
   
   

   3. E ∝	1
      	r3

   
   
   

   4. E ∝	1
      	r4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Intensity of electric field due to a Dipole
   

   (E) =	p	√3 cos² θ + 1 ⇒ E ∝	1
   	4πε0r3		r3

   Correct Option: C

   Intensity of electric field due to a Dipole
   

   (E) =	p	√3 cos² θ + 1 ⇒ E ∝	1
   	4πε0r3		r3

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33. From a point charge, there is a fixed point A. At A, there is an electric field of 500 V/m and potential difference of 3000 V. Distance between point charge and A will be​​
    

1. 1. 6 m

   
   
   

   2. 12 m

   
   
   

   3. 16 m

   
   
   

   4. 24 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given : Electric field (E) = 500 V/m ​and potential difference (V) = 3000 V. ​
   

   We know that electric field (E) = 500 =	V	or d =	3000	= 6 m
   	d		500

   
   [where d = Distance between point chargeand A]

   Correct Option: A

   Given : Electric field (E) = 500 V/m ​and potential difference (V) = 3000 V. ​
   

   We know that electric field (E) = 500 =	V	or d =	3000	= 6 m
   	d		500

   
   [where d = Distance between point chargeand A]

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34. 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​​
    

1. 1. p^–1 and r^–2

   
   
   

   2. p and r^–2

   
   
   

   3. p² and r^–3

   
   
   

   4. p and r^–3

   
   
   

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1. View Hint View Answer Discuss in Forum

   E =	p
   	4πε0r3

   
   

   Apparently, E ∝ p  and E ∝	1	∝ r3
   	r3

   Correct Option: D

   E =	p
   	4πε0r3

   
   

   Apparently, E ∝ p  and E ∝	1	∝ r3
   	r3

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35. A hollow insulated conduction sphere is given a positive charge of 10 µC. What will be the electric field at the centre of the sphere if its radius is 2 metres?
    

1. 1. zero

   
   
   

   2. 5 µCm^–2

   
   
   

   3. 20 µCm^–2

   
   
   

   4. 8 µCm^–2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Charge resides on the outer surface of a conducting hollow sphere of radius R. We consider a spherical surface of radius r < R. ​
   By Gauss's theorem,
   
   

   ∮E→ . ds→ =	1	× charge enclosed
   	ε0

   
   

   or E.4πr2 =	1	× 0 ⇒ E = 0
   	ε0

   
   i.e. electric field inside a hollow sphere is zero.

   Correct Option: A

   Charge resides on the outer surface of a conducting hollow sphere of radius R. We consider a spherical surface of radius r < R. ​
   By Gauss's theorem,
   
   

   ∮E→ . ds→ =	1	× charge enclosed
   	ε0

   
   

   or E.4πr2 =	1	× 0 ⇒ E = 0
   	ε0

   
   i.e. electric field inside a hollow sphere is zero.

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