6. As per the diagram, a point charge +q is placed at the origin O. Work done in taking another point charge – Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is:
   

1. 1. zero

   
   
   

   2. 	-qQ	1		√2a
      	4πε0	a²

   
   
   

   3. 	qQ	1		.	a
      	4πε0	a²			√2

   
   
   

   4. 	qQ	1		√2a
      	4πε0	a²

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that potential energy of two charge system is given by ​
   

   U =	1	=	q1q2
   	4πε0		r

   
   ​According to question, ​
   

   UA =	1		(+q)(-Q)	= -	1		Qq
   	4πε0		a		4πε0		a

   
   

   and UB =	1		(+q)(-Q)	= -	1		Qq
   	4πε0		a		4πε0		a

   
   ​∆U = U_B – U_A = 0​​ ​
   We know that for conservative force, ​
   W = –∆U = 0

   Correct Option: A

   We know that potential energy of two charge system is given by ​
   

   U =	1	=	q1q2
   	4πε0		r

   
   ​According to question, ​
   

   UA =	1		(+q)(-Q)	= -	1		Qq
   	4πε0		a		4πε0		a

   
   

   and UB =	1		(+q)(-Q)	= -	1		Qq
   	4πε0		a		4πε0		a

   
   ​∆U = U_B – U_A = 0​​ ​
   We know that for conservative force, ​
   W = –∆U = 0

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7. A bullet of mass 2 g is having a charge of 2µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?

1. 1. 50 V

   
   
   

   2. 5 kV

   
   
   

   3. 50 kV

   
   
   

   4. 5 V

   
   
   

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1. View Hint View Answer Discuss in Forum

   qV =	1	mv²
   	2

   
   

   ⇒ 2 × 10-6 × V =	1	×	2	× 10 × 10
   	2		1000

   
   ∴  V = 50 kV

   Correct Option: C

   qV =	1	mv²
   	2

   
   

   ⇒ 2 × 10-6 × V =	1	×	2	× 10 × 10
   	2		1000

   
   ∴  V = 50 kV

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8. A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is

1. 1. qEy²

   
   
   

   2. qE²y

   
   
   

   3. qEy

   
   
   

   4. q²Ey

   
   
   

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1. View Hint View Answer Discuss in Forum

   K.E. = Force × distance  = qE.y

   Correct Option: C

   K.E. = Force × distance  = qE.y

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9. Each corner of a cube of side l has a negative charge, –q. The electrostatic potential energy of a charge q at the centre of the cube is

1. 1. 4q²

      √2πε0l

   
   
   

   2. √2q²

      4πε0l

   
   
   

   3. 4q²

      √2πε0l

   
   
   

   4. -	4q²
      	√3πε0l

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​Length of body diagonal = ​√3l
   ∴ Distance of centre of cube from each corner ​
   

   r =	√3	l
   	2

   
   ​P.E. at centre ​
   = 8 × Potential Energy due to A ​
   

   = 8 ×	√3	l
   	2

   
   

   = 8 ×	1	× 2 × q × (-q) =	-4q²
   	4πε0√3l		√3πε0l

   
   

   Correct Option: D

   ​Length of body diagonal = ​√3l
   ∴ Distance of centre of cube from each corner ​
   

   r =	√3	l
   	2

   
   ​P.E. at centre ​
   = 8 × Potential Energy due to A ​
   

   = 8 ×	√3	l
   	2

   
   

   = 8 ×	1	× 2 × q × (-q) =	-4q²
   	4πε0√3l		√3πε0l

   
   

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10. A solid spherical conductor is given a charge. The electrostatic potential of the conductor is

1. 1. constant throughout the conductor

   
   
   

   2. largest at the centre

   
   
   

   3. largest on the surface

   
   
   

   4. largest somewhere between the centre and the surface

   
   
   

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1. View Hint View Answer Discuss in Forum

   Electric potential is constant ​(equal to kq/R ,where k = 1/4πε₀) ​
   within or on the surface of conductor.

   Correct Option: A

   Electric potential is constant ​(equal to kq/R ,where k = 1/4πε₀) ​
   within or on the surface of conductor.

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