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Question Bank No: 2

1. Two charges +4q and +q are placed at the ends of a straight line. A charge -q is placed at the mid-point of this line. Then the charge +q will be in

a)		stable equilibrium
b)		unstable equilibrium
c)		non-equilibrium state
d)		none of the above mentioned states

2. The charge on the uranium nucleus is 1.5 $\times 10^{- 17}$ C and the charge on the $α - particle is 3.2 \times 10^{- 19} c$ .The electrostatic force between a uranium nucleus and an $α -$ particle separated by 2.0 $\times 10^{- 13} m$ is approximately

a)		1.1 $\times 10^{- 33} N$
b)		1.1 $\times 10^{- 20} N$
c)		1.1 $\times 10^{- 13} N$
d)		1.1N

3. A uniform electric field exists in the vertically downward direction. The magnitude is 10N $C^{- 1} .$ What is the increase in electrostatic potential as one goes up through a height of 50cm?

a)		20V
b)		15V
c)		10V
d)		5V

4. A long cylindrical wire carries a positive charge of linear density 2.0 $\times 10^{- 8} {cm}^{- 1} .$ An electron revolves around it in a circualr path under the influence of the attractive electostatic force. What is the kinetic energy of the electron?

a)		3 $\times 10^{- 16} j$
b)		3 $\times 10^{- 17} j$
c)		3 $\times 10^{- 18} j$
d)		3 $\times 10^{- 15} j$

5. The electric potential V in an electric field is given by V= $\frac{1}{4 π \in_{0}} .$ $\frac{q}{r} . T he electric field at a point \vec{r}$ =2i+6j 3k is given by

a)		$\frac{1}{2 i + 6 j + 3 k}$ . $\frac{1}{4 \in_{0}} . \frac{a}{r}$
b)		$\frac{1}{4 π \in_{0}} . \frac{q}{r} \frac{2 i + 6 j + 3 k}{49}$
c)		$\frac{1}{4 π \in_{0}} . q \frac{2 i + 6 j + 3 k}{343}$
d)		$\frac{1}{4 π \in_{0}} . \frac{q}{r} 2 i + 6 j + 3 k$

6. The excess (equal in number) of electrons that must be placed on each of two small spheres spaced 3cm apart, so that force of repulsion between the spheres to be $10^{- 19} N is$

a)		25
b)		225
c)		625
d)		1250

7. Three plates each of area 50 ${cm}^{2}$ seperated from each other by a distnace of 3 mm are connected to a source of emf of 120 V. Then the energy stored when plates are fully charged
electstat-q29

a)		0.2 J
b)		5 J
c)		1.6 J
d)		7 J

8. A technician has only two capacitors . By using these sungly, in series or in parallel, he is able to obtain the capacitance of 3 $μ$ F, 4 $μ$ F, 12 $μ$ F, 16 $μ F$ . What are the capacitance of capacitors?

a)		6 $μ$ F and 10 $μ$ F
b)		7 $μ$ F and 9 $μ$ F
c)		4 $μ$ F and 12 $μ$ F
d)		4 $μ$ F and 16 $μ$ F

9. The air between the plates of a parallel plate capacitor is replaced by a medium of dielectric constant K. The p.d. b/w the plate becom

a)		K times
b)		$\frac{1}{K}$ times
c)		$\sqrt{K}$ times
d)		$\frac{1}{\sqrt{K}}$ times

10. A parallel plate capacitor is charged and then isolated. What is the effect on increasing the plate separation?
$\begin{matrix} Charge & Potential & Capacitance \end{matrix}$

a)		Constant constant decrease
b)		Increase increase decrease
c)		Constant decrease increase
d)		Constant increase decrease

11. The electric field outside a charged long straight wire by E = 1,000/rV $m^{- 1}$ , and is directed outwards. What is the sign of the charge on the wire? If two points A and B are situated such that $r_{A}$ =0.2 abd $r_{B}$ =034 m. The value of $V_{B} - V_{A}$ is

a)		+ charge, -693.1 V $m^{- 1}$
b)		- charge, 693.1 V $m^{- 1}$
c)		+ charge, -963.1 V $m^{- 1}$
d)		- charge, 963.1 V $m^{- 1}$

12. When two uncharged metal balls of radius 0.09 mm each collide, one electron is transferrred between them. The potential difference between them would be

a)		16 $μ$ V
b)		16pV
c)		32 $μ$ V
d)		32pV

13. The figure shows a charge q placed at the centre of a hemispher, a second charge Q is placed at one of the positions A, B, C and D. In which position(s) of the second charge the electric flux through the hemisphere remains and charged?
electstat-q22

a)		A
b)		B
c)		C
d)		D

14. Point A and B lie on the equatorial line of a dipole of dipole moment p at a distance 'd' as shown in the figure. What is the work done in moving a charge q from A to B following a semi circular path in the field of the dipole?
electstat-q21

a)		2q $E_{eq}$
b)		- 2q $E_{eq}$
c)		zero
d)		$q^{2}$ $E_{eq}$ d

15. An electric dipole placed with its axis at $30^{o}$ with a uniform electrical field experiences a torque of 0.032 Nm. If the dipole were free to rotate, its potential energy in the stable equilibrium would be

a)		0.064 J
b)		-0.064 J
c)		zero
d)		0.16 J

16. In a certain region an uniform electric field E = $E_{x}$ i exists. If a small circle is drawn with the origin as centre cutting the axes at A (a, 0), B (0, a), C (-a, 0) and D (0, -a), the potential is maximum at

a)		A
b)		B
c)		C
d)		D

17. Two identical thin rings, each of radius R meters are coaxially placed at distance R meters apart. If $Q_{1}$ and $Q_{2}$ are respectively the charges uniformly distributed on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is

a)		zero
b)		$\frac{1}{4 π \in_{0}}$ $\frac{q (Q_{1} - Q_{2}) (\sqrt{2} - 1)}{\sqrt{2} R}$
c)		$\frac{1}{4 π \in_{0}} \frac{\sqrt{2 q (Q_{1} + Q_{2})}}{R}$
d)		$\frac{1}{4 π \in_{0}}$ $\frac{q (Q_{1} + Q_{2}) (\sqrt{2} + 1)}{\sqrt{2} R}$

18. Five charges 'q' each are placed at the five corners A, B, C, D and E of a regular hexagon ABCEDEF of side 'a' then the electric field intensity at the centre O of the hexagon is

a)		$\frac{1}{4 π \in_{0}}$ $\frac{q}{a^{2}}$ along $\vec{O} F$
b)		$\frac{1}{4 π \in_{0}}$ $\frac{q}{a^{2}}$ along $\vec{F} O$
c)		$\frac{1}{4 π \in_{0}}$ $\frac{q}{{3 a}^{2}}$ along $\vec{O} F .$
d)		$\frac{1}{4 π \in_{0}}$ $\frac{5 q}{a^{2}}$ along $\vec{O} F .$

19. Two equal positive charges are kept at point A and B. While moving from A to B, the electric potential

a)		increases continuously
b)		decreases and then increases
c)		decreases continuously
d)		increases and then decreases

20. A sphere of 4 cm radius is suspended within a hallow sphere of radius of 6 cm. The inner sphere is charged to a potential 3 e.s.u. When the outer sphere is earthed. The charge on the inner sphere is

a)		54 esu
b)		1/4 esu
c)		30 esu
d)		36 esu

21. If the dielectric constant and dielectric strength be denoted by K and X respectively. Then the material suitable for use as a dielectric in a capacitor must have

a)		high K and high X
b)		low K and high X
c)		high K and low X
d)		low K and low X

22. A point charge of 60 stat coulomb is placed 3 cms in front of an earthed metallic plates of large size. Then the force of attraction on the point charge is

a)		100 dynes
b)		360 dynes
c)		400 dynes
d)		180 dynes

23. Two free protons which are separated by a distance of $10^{- 10}$ metres, are released, then the kinetic energy of each proton when at infinite separation is

a)		23 $\times 10^{- 19}$ J
b)		46 $\times 10^{- 19}$ J
c)		11.5 $\times 10^{- 19}$ J
d)		5.6 $\times 10^{- 19}$ J

24. An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle $π$ /3 with the X-axis. If the electric field at P makes an angle $θ$ with the X-axis, the value of $θ$ would be

a)		$π$ /3
b)		2 $π$ /3
c)		$π$ /3 + $\tan^{- 1}$ ( $\sqrt{3}$ /2)
d)		$\tan^{- 1}$ ( $\sqrt{3}$ /2)

25. A thin spherical shell of radius 'a' carries a charge 'q'. Concentric with it is another thin metallic spherical shell of radiuus b (>a). When outer shell is given a charge Q the electric field at point C at distance c (a < c > b) is

a)		$\frac{Kq}{a^{2}}$
b)		$\frac{Kq}{b^{2}}$
c)		$\frac{Kq}{c^{2}}$
d)		$\frac{K (q + Q)}{a^{2}}$

26. A cube of side 'a' is placed in uniform electric field E = $E_{0} i$ . The total electric flux through the cube is
electstat-q9

a)		zero
b)		2 $a^{2} \in_{0}$
c)		4 $a^{2} \in_{0}$
d)		6 $a^{2} \in_{0}$

27. Electric charges (q, q, -2q) are placed at the centers of an equilateral triangle ABC of side l. The magnitude of the dipole moment of the system is

a)		4ql
b)		$\sqrt{3}$ ql
c)		2ql
d)		ql

28. Two identical conducting spheres of radius 0.15 m are separated by a distance 10 m. What is the charge on each sphere if the potential of the spheres are +1500 V and -1500 V respectively ?

a)		2.6 $\times 10^{- 6}$ C
b)		2.6 $\times 10^{- 7}$ C
c)		2.6 $\times 10^{- 8}$ C
d)		2.6 $\times 10^{- 9}$ C

29. Identical charges +q are placed at the corners of regular hexagon. The value of the charge Q at the centre of the hexagon to make whole system of charge at equilibrium is

a)		1.83q
b)		-1.83q
c)		8.31q
d)		-8.31q

30. Consider a charged filament (charge per unit length $λ$ ) of length l. Consider a point P at distance 'a' from the filament. The elecrostatic field at P due to this filament in the limit $a ≪$ 1will correspond to that due to

a)		an infinitely long filament
b)		a semi-infinite filament
c)		a point charge
d)		a semi-circular charge (with P as the centre)

31. A positive charge of 9 $μ$ C is fixed at the origin. A second charge Q is fixed on the x- axis at x = a. A charge $q_{0}$ at x=3a does not experience any net force. What is value of q?

a)		$-$ 4 $μ C$
b)		+4 $μ C$
c)		+2 $μ C$
d)		$-$ 2 $μ C$

32. Find the dipole moment of a charge distributed uniformly over the surface of a spherical shell of radius R. One hemispherical shell has a charge Q while the charge on the other is equal to -Q

a)		4 QR
b)		2QR
c)		QR
d)		QR/2

33. Two completely ionised carbon 12 atom (q=6e) are brought to a distance of 10 Frmi of each other. What is the force of repulsion?

a)		83 N
b)		83 mN
c)		83 $μ N$
d)		83 nN

34. Two insulated charged spheres of radii 70 cm and 75 cm respectively and having equal charge q are connected by a copper wire and then they are seperated

a)		both the spheres will have same charge q
b)		the charge on 70 cm sphere will be greater than that on the 75 cm sphere
c)		the charge on 75cm sphere will be greater than that on the 70 cm sphere
d)		both will have zero charge

35. Six metallic plates each of surface area of one side A are placed at a distance d from each other. The alternative plates are connected to P and Q. The capacitance of the system between P and Q is

a)		$\frac{\sum_{0} A}{d}$
b)		$\frac{5 \sum_{0} A}{d}$
c)		$\frac{6 \sum_{0} A}{d}$
d)		$\frac{\sum_{0} A}{d}$

36. A condenser of capacitance 6 $μ F$ was originally charged to 10 V. Now the p.d is made 20 V. increase in potential energy is

a)		${3 \times 10}^{- 4} J$
b)		${6 \times 10}^{- 4} J$
c)		${9 \times 10}^{- 4} J$
d)		${12 \times 10}^{- 4} J$

37. Three capacitors of capacities 3 $μ F$ , 9 $μ F$ and 18 $μ F$ are connected first in series and then in parallel. The ratio of the equivalent capacities in the two cases

a)		1 : 15
b)		15 : 1
c)		1 : 1
d)		1 : 3

38. Four capacitors each of capacitance 4 $μ F$ are connected as shown in the figure. If $V_{p} - V_{q} = 15 V$ , the energy stored in the system in Joules is
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a)		${2.4 \times 10}^{- 7}$
b)		${1.8 \times 10}^{- 4}$
c)		${3.6 \times 10}^{- 7}$
d)		${5.4 \times 10}^{- 7}$

39. A 500 $μ F$ capacitor is charged at a steady rate of 100 $μ C / s$ . The potential difference across the capacitor will be 10V after an interval of

a)		2.5 s
b)		9 s
c)		20 s
d)		50 s

40. 1000 small water drops each of radius r and charge q coalesce to form one spherical drop. The potential of the big drop is larger than that of smaller one by a factor

a)		1000
b)		100
c)		10
d)		1

41. Charges + $(\frac{10}{3})$ $\times 10^{- 9}$ C are placed at each of the four corners of a square of side 8cm. The potential at the intersection of the diagonals is

a)		$150 \sqrt{2} V$
b)		$1500 \sqrt{2} V$
c)		$900 \sqrt{2} V$
d)		900 V

42. Three equal capacitors each of capacitance C are connected as shown in the fig. The equivalent capacitance between A and B
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a)		3C
b)		C
c)		C/3
d)		$\frac{3}{2}$ C

43. The electric potential V as a function of distance x in metres is given by V = ( ${5 x}^{2} - 10 x - 9$ ) volt. The value of electric field at x = 1m would be

a)		20 V/m
b)		6 V/m
c)		zero
d)		11 V/m

44. When a capacitor having capacitance $4 μ F$ and p.d 100V is discharged the energy released in Joule is

a)		0.2
b)		0.02
c)		0.04
d)		0.025

45. A capacitor 60pF has charge ${3 \times 10}^{- 8} C$ . The energy stored in it is

a)		${15 \times 10}^{- 6} J$
b)		${7.5 \times 10}^{- 6} J$
c)		${2.4 \times 10}^{- 6} J$
d)		1.2 eV

46. The kinetic energy of an electron which is accelerated through a potential of 100 V is

a)		${1.6 \times 10}^{- 17} J$
b)		${1.6 \times 10}^{17} J$
c)		${6.6 \times 10}^{- 34} J$
d)		100 J

47. A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at the centre of the sphere is

a)		zero
b)		10 V
c)		same as at a point 5 cm away from the surface
d)		same as at a point 25 cm away from the surface

48. State which one of the following is correct

a)		joule = coulomb $\times$ volt
b)		joule = coulomb / volt
c)		joule = volt/ ampere
d)		joule = volt $\times ({ampere}^{2})$

49. Inside a hollow charged spherical conductor the potential

a)		is constant
b)		varies directly as the distance from the centre
c)		varies inversely as the distance from the centre
d)		varies inversely as the square of the distance from the centre

50. The electrical field intensity at a point and potential are related as

a)		E = $\frac{q}{V}$
b)		E = $\frac{d q}{d v}$
c)		E = $+ \frac{d v}{d r}$
d)		none of the above