The displacement of a charge Q in the electric field E=e1i^+e2j^+e3k^ is r^=ai^+bj^. The work done is 

(1) Q(ae1+be2)

(2) Q(ae1)2+(be2)2

(3) Q(e1+e2)a2+b2

(4) Q(e12+e22)(a+b)

Subtopic:  Electric Potential Energy |
 60%
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Three charges Q, +q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

(1) q1+2

(2) 2q2+2

(3) –2q

(4) +q

Subtopic:  Electric Potential Energy |
 70%
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A cube of a metal is given a positive charge \(Q\). For the above system, which of the following statements is true?
1. Electric potential at the surface of the cube is zero.
2. Electric potential within the cube is zero.
3. Electric field is normal to the surface of the cube.
4. Electric field varies within the cube.
Subtopic:  Equipotential Surfaces |
 77%
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Three charges \(Q\)\(+q \) and \(+q \) are placed at the vertices of an equilateral triangle of side \(l\) as shown in the figure. If the net electrostatic energy of the system is zero, then \(Q\) is equal to:

1. \(-\frac{q}{2} \) 2. \(-q\)
3. \(+q\) 4. \(\text{zero}\)
Subtopic:  Electric Potential Energy |
 73%
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Electric potential at any point is V=5x+3y+15z, then the magnitude of the electric field is

(1) 32

(2) 42

(3) 52

(4) 7

Subtopic:  Relation between Field & Potential |
 74%
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Kinetic energy of an electron accelerated in a potential difference of 100 V is 

(1) 1.6 × 10–17 J

(2) 1.6 × 1021 J

(3) 1.6 × 10–29 J

(4) 1.6 × 10–34 J

Subtopic:  Electric Potential Energy |
 88%
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If identical charges (–q) are placed at each corner of a cube of side b, then electric potential energy of charge (+q) which is placed at centre of the cube will be -

(1) 82q24πε0b

(2) 82q2πε0b

(3) 42q2πε0b

(4) 4q23πε0b

Subtopic:  Electric Potential Energy |
 59%
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A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be -

(1) 1840 keV

(2) 1/1840 keV

(3) 1 keV

(4) 920 keV

Subtopic:  Electric Potential |
 70%
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A thin spherical conducting shell of radius \(R\) has a charge \(q.\) Another charge \(Q\) is placed at the centre of the shell. The electrostatic potential at a point \(P\) which is at a distance \(\frac{R}{2}\) from the centre of the shell is:
1. \(\frac{\left( q + Q \right)}{4 \pi \varepsilon_{0}} \frac{2}{R}\)
2. \(\frac{2 Q}{4 \pi \varepsilon_{0} R}\)
3. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} - \frac{2 q}{4 \pi \varepsilon_{0} R}\)
4. \(\frac{2 Q}{4 \pi \varepsilon_{0} R} + \frac{q}{4 \pi \varepsilon_{0} R}\)

Subtopic:  Electric Potential |
 62%
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A charge of \(10\) e.s.u. is placed at a distance of \(2\) cm from a charge of \(40\) e.s.u. and \(4\) cm from another charge of \(20\) e.s.u. The potential energy of the charge \(10\) e.s.u. is: (in ergs) 

1. \(87.5\) 2. \(112.5\)
3. \(150\) 4. \(250\)
Subtopic:  Electric Potential Energy |
 58%
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