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Question Bank No: 1

1. Two particles each of mass m and carrying charge Q are seperated by some distance. If they are in equillibrium under mutual gravitational and electrostatic forces, then Q/m (inc/kg) is of the order

a)		$10^{- 5}$
b)		$10^{- 10}$
c)		$10^{- 15}$
d)		$10^{- 20}$

2. A 10 $μ F$ capacitor is charged to a potential differences of 1000V. The terminals of the charged capacitor are disconnected from the power supply and connected to a terminals of an uncharged 6 $μ F$ capacitor. What is the final potential difference across each capacitor

a)		167 V
b)		100V
c)		625V
d)		250V

3. Metalic sphere of radius R is charged to potential V. Then charge q is proportional to

a)		V
b)		R
c)		both
d)		None

4. A force of 40N is acting between two charges in air. If the space between them is filled with glass of K =8. What will be the force

a)		5N
b)		15N
c)		200N
d)		40N

5. On moving charge of 20C by 2cm, 2joule of work is done, then the potential difference between the points is

a)		8V
b)		2V
c)		0.1V
d)		0.5V

6. A dipole with moment $\vec{p}$ is placed in uniform electric field $\vec{E} .$ Then torque acting on it is given

a)		$\vec{τ} = \vec{p} . \vec{E}$
b)		$\vec{τ} = \vec{p} \times \vec{E}$
c)		$\vec{τ} = \vec{p} + \vec{E}$
d)		$\vec{τ} = \vec{p} - \vec{E}$

7. An $α$ particle and a proton are accelerated through same potential difference from rest. Find the ratio of their final velocities.

a)		$\sqrt{2} : 1$
b)		1:1
c)		1: $\sqrt{2}$
d)		1:2

8. A charge Q is placed at the corner of a cube. The electric flux through all the six faces of the cube is

a)		$φ$ /6 $ε_{0}$
b)		$φ$ /8 $ε_{0}$
c)		$φ$ / $ε_{0}$
d)		$φ$ /3 $ε_{0}$

9. If electric field in a region is radially outward with magnitude E =Ar, the charge contained in a sphere of radius r entered at the origin is

a)		$\frac{1}{4 π ε_{0}} A r_{0}^{3}$
b)		4 $π ε_{0} A r^{3}$
c)		$\frac{1}{4 π ε_{0}} \frac{A}{r_{0}^{3}}$
d)		$\frac{4 π ε_{0} A}{r_{0}^{3}}$

10. In bringing an electron towards another electron, the electrostatic potential energy of the system.

a)		remains same
b)		becomes zero
c)		increases
d)		decreases

11. Eight dipoles of charges of magnitude 'e' are placed inside a cube. The total electric flux coming out of the cube will be

a)		$\frac{8 e}{ε_{0}}$
b)		$\frac{16 e}{ε_{0}}$
c)		$\frac{e}{ε_{0}}$
d)		zero

12. On $α$ particle is accelerated through potential difference of $10^{6} Volt .$ Its K.E will be

a)		MeV
b)		2 MeV
c)		4 MeV
d)		8 MeV

13. A hollow metal sphere of radius 10cm is charged such that the potential on its surface is 80V. The potential at the centre of the sphere is

a)		zero
b)		80V
c)		800V
d)		8V

14. A thin metal plate M is inserted between the plates of a parallel plate capacitor as shown in fig. The new capacitance in terms of initial capacitance C is
electrostaticsQ15

a)		2 C
b)		C/2
c)		C
d)		infinity

15. A one micro farad capacitor of a TV is subjected to 4000V potential difference. The energy stored in capacitor is

a)		8J
b)		16J
c)		4 $\times 10^{- 3} J$
d)		2 $\times 10^{- 3} J$

16. The diameter of the plate of parallel plate condenser is 6cm. If its capacity is equal to that of a sphere of diameter 200cm, the separation between the plates of the condenser is

a)		4.5 $\times 10^{- 4} m$
b)		2.25 $\times 10^{- 4} m$
c)		6.75 $\times 10^{- 4} m$
d)		9 $\times 10^{- 4} m$

17. A capacitor works in

a)		AC circuit
b)		DC circuit
c)		both a and b
d)		neither 'a' nor 'b'

18. 64 identical drops og Hg are charged simultaneously to the same potential of 10Volt. Assuming the drops to be spherical, if all the charged drops are made to combine to form one large drop, then its potential will be

a)		100 units
b)		320 units
c)		640 units
d)		160 units

19. In a region of space having a uniform electric field E, a hemi spherical bowl of radius r is placed. The electric flux $φ$ through the boul is

a)		2 $π rE$
b)		4 $π r^{2} E$
c)		2 $π r^{2} E$
d)		$π r^{2} E$

20. An electric cell does 5J of work in carrying 10C charge around closed circuit.The electro motive force of the cell is

a)		2V
b)		0.5V
c)		4V
d)		1V

21. The electric potential V at any instant (x,y,z) in space is given by V=4 $x^{2} volt .$ The electric field at (1,0,2)m in V $m^{- 1}$ is

a)		8, along negative x-axis
b)		8, along positive x-axis
c)		16 along negative x-axis
d)		16 along positive z- axis

22. An electron of mass m and charge e is accelerated from rest through a potential difference V in vaccum. Its final speed will be

a)		$\frac{\sqrt{2 eV}}{m}$
b)		$\sqrt{\frac{eV}{m}}$
c)		eV/2m
d)		eV/m

23. The plates of a capacitor are separated by 5mm. A battery of 1KV is connected across them. The force experienced by a electron located in between the plates is

a)		3.2 $\times 10^{- 14} N$
b)		1.6 $\times 10^{- 19} N$
c)		3.2 $\times 10^{- 24} N$
d)		1.6 $\times 10^{- 14} N$

24. There is an electric field E in X direction. If the workdone on moving a charge of 0.2C through a distance of 2m. along a line making an angle $60^{0}$ with x axis is 4J. Then what is the value of E?

a)		$\sqrt{3} N / C$
b)		4N/C
c)		5N/C
d)		20N/C

25. The electric field strength at a distance r from a point charge Q is E. What will be electric field strength if the distance of observation point is increased bt 2r?

a)		E/2
b)		E/4
c)		E/5
d)		none of the above

26. A body has negative charge of 1coulomb. It means that

a)		It has lost one electron
b)		It has acquired one additional electron
c)		It has lost 6.25 $\times 10^{18}$ electrons
d)		It has acquired 6.25 $\times 10^{18}$ additional electrons

27. The ratio of the force between charges in vacuum at a certain distance apart to that between the same charges, the same distance apart in a medium of permitivity $ε$ is

a)		$ϵ : 1$
b)		1: $ϵ$
c)		$ϵ : ϵ_{0}$
d)		none of these

28. The dielectric constant K of an insulator can be

a)		-1
b)		0
c)		0.5
d)		5

29. Equivalent capacitance b/w A and B of the network is
electrostatics-q28

a)		2 $μ F$
b)		1 $μ F$
c)		3 $μ F$
d)		1.5F

30. A charged parallel plate capacitor has capacitance C and energy W. When a dielectric slab of dielectric constant 6 is placed b/w the plates, the capacitance and energy becomes

a)		6C and 6W
b)		6C and W/6
c)		C/6 and W/6
d)		C/6 and 6W respectively

31. Two spherical conductors of capacitance 3.0 $μ F$ and 5 $μ F$ are charged to potential of 300V and 500V. The two are connected resulting in redistribution of charges. The final charge on smaller conductor

a)		900 $μ C$
b)		1275 $μ C$
c)		2125 $μ C$
d)		2500 $μ C$

32. 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

33. A and B are two spherical conductors of the same external size. A is solid and B is hollow. Both are charged to the same potential. If the charges, on A and B are $Q_{A}$ and $Q_{B} . Then$

a)		$Q_{A} > Q_{B}$
b)		$Q_{A}$ = $Q_{B}$
c)		$Q_{A} < Q_{B}$
d)		none of these

34. The electric potential V at any point (x,y,z) in space is given by V=4 $x^{2}$ volt. The electric field at the point (1m,0,2m) is

a)		8V $m^{- 1} along - ve X - direction$
b)		80 V $m^{- 1} along - ve X - direction$
c)		0.8 V $m^{- 1} along - ve X - direction$
d)		800 V $m^{- 1} along - ve X - direction$

35. The field at a distance r from a long string of charge per unit length $λ is$

a)		$\frac{K λ}{r^{2}}$
b)		$\frac{K λ}{r}$
c)		$\frac{K λ}{2 r}$
d)		$\frac{2 K λ}{r}$

36. A parallel plate capacitor is charged upto 100V. A 2 mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the plate is increased by 1.6 mm. The dielectric constant of the plate is

a)		5
b)		1.25
c)		4
d)		2.5

37. A point charge +q is placed near a surface element of area ds which subtends a solid angle d $ω$ steradian then the total normal electric flow through the surface element is

a)		$\frac{q}{\in_{0}} [\frac{4 n}{d ω}]$
b)		$\frac{q}{\in_{0}} [\frac{d ω}{4 n}]$
c)		$\frac{q}{\in_{0}} ds$
d)		$\frac{q}{\in_{0}} d ω$

38. A point charge at any point on the axis of an electric dipole at some large distance experience a force F. The force acting on the point when its distance from the dipole is doubled

a)		2F
b)		F/2
c)		F/4
d)		F/8

39. Four equal charges of Q each are placed at the four corners of a square of side 'a' metres. The work done in removing a charge -Q coulomb from its centre to infinity is

a)		zero
b)		$\frac{\sqrt{2}}{4 π \in_{0}} \frac{Q^{2}}{a}$
c)		$\frac{\sqrt{2}}{π \in_{0}} \frac{Q^{2}}{a}$
d)		$\frac{Q^{2}}{2 π \in_{0} a}$

40. A metal sphere A of radius 'a' is charged to potential V. What will be its potential if it is enclosed by a spherical conducting shell B of radius b and the two are connected by a wire

a)		$\frac{a}{b} V$
b)		$\frac{a + b}{a} V$
c)		$\frac{b}{a} V$
d)		$\frac{b}{a + b} V$

41. Two small balls having equal +Q charge each and mass m each are suspended by two insulating strings of equal length L from a hook fixed to a stand. The whole setup is in a region outside the gravitational field of earth. In equilibrium the tension in each string is

a)		$\frac{1}{4 π \in_{0}} \frac{Q^{2}}{L^{2}}$
b)		$\frac{1}{4 π \in_{0}} \frac{Q^{2}}{{4 L}^{2}}$
c)		$\frac{1}{4 π \in_{0}} \frac{Q^{2}}{2 L^{2}}$
d)		$\frac{1}{4 π \in_{0}} \frac{2 Q^{2}}{L^{2}}$

42. The electric potential V at any point (x,y,z) all in metres in space is given by
v=4 $x^{2} .$ Then the electric field E at point (1,0,2) is

a)		8 V $m^{- 1}$ along the +ve X-direction
b)		8V $m^{- 1}$ along the -ve X-direction
c)		4V $m^{- 1} along - ve X - direction$
d)		zero

43. An electron of mass $m_{e}$ initially at rest moves through a certain distance in uniform electric field in time $t_{1} . A proton of mass m_{p}$ also initially at rest takes time $t_{2}$ to move through an equal distance in this uniform electric field, the ratio of $t_{2} / t_{1}$ is nearly equal to (neglect effect of g)

a)		1
b)		$\sqrt{\frac{m_{p}}{m_{e}}}$
c)		$\sqrt{\frac{m_{e}}{m_{p}}}$
d)		1836

44. Two point charges placed at a distance of 20cm in air repel each other with a certain force when dielectric slab of thickness 8cm and dielectric constant k is introduced between these point charges, force of interaction becomes 1/9th of its previous value. The K is approximately

a)		36
b)		46
c)		3
d)		4

45. An electron enters with velocity of 5 $\times 10^{6} {ms}^{- 1}$ along the +ve direction of an electric field of intensity $10^{3} N C^{- 1.}$ If mass of the electron is 9.1 $\times 10^{- 31}$ Kg, then the time taken by the electron to come temporarily to rest is

a)		5.8 $\times 10^{8} \sec$
b)		infinite
c)		1.45 $\times 10^{- 8}$ sec
d)		2.9 $\times 10^{- 8}$ sec

46. ABC is a right angled triangle, AB=3cms, BC=4cms, AC=5cms and changes +15, +12,-20 e.s.u are placed at ABC respectively, the workdone in moving the three charges to infinite separation is

a)		100 ergs
b)		+60 ergs
c)		60 ergs
d)		(20+15-20)ergs

47. Two thin hollow conducting spheres of radii $R_{1}$ and $R_{2}$ are placed concentrically, charges on the two are $Q_{1}$ and $Q_{2}$ respectively. If $R_{1} > R_{2}$ then the potential at a pt. Distant r from the centre when $R_{1} > r > R_{2} is$

a)		$\frac{1}{4 π \in_{0}} (\frac{Q_{1}}{r} + \frac{Q_{2}}{r})$
b)		$\frac{1}{4 π \in_{0}} (\frac{Q_{1}}{r} + \frac{Q_{2}}{R_{2}})$
c)		$\frac{1}{4 π \in_{0}} (\frac{Q_{1}}{R_{1}} + \frac{Q_{2}}{R_{2}})$
d)		$\frac{1}{4 π \in_{0}} (\frac{Q_{1}}{R_{1}} + \frac{Q_{2}}{r})$

48. A conducting hollow spherical shell having an inner radius 'a' and outer radius 'b' carries a charge Q. If a point charge q is placed at the center of the sphere then surface charge density at the outer surface is

a)		$\frac{q}{4 π b^{2}}$
b)		$\frac{- q}{4 π b^{2}}$
c)		$\frac{Q + q}{4 π (b^{2} - a^{2})}$
d)		$\frac{Q + q}{4 π b^{2}}$

49. A proton is released from rest at a distance of $10^{- 4} A^{0}$ from the nucleus of mercury atom (Z=80). The K.E. of the proton when it is far away from the nucleus is

a)		12eV
b)		12KeV
c)		1.2MeV
d)		12Mev

50. An electric diploe of moment p is placed at the origin along the X-axis. The electric field at a point P, whose position vector makes an angle $θ$ with X-axis, will make an angle $φ$ with the X-axis where $φ = θ + α with α = \tan^{- 1} (1 / 2 \tan θ)$ we have

a)		$φ = θ + 3 α$
b)		$φ = θ + 2 α$
c)		$φ = θ + α$
d)		$φ = θ$