Electrostatics Test 8

Total Questions:50 Total Time: 75 Min

Remaining:

 

Questions 1 of 50

Question:An isolated solid metallic sphere is given \( + Q\) charge. The charge will be distributed on the sphere

Answers Choices:

Uniformly but only on surface

Only on surface but non-uniformly

Uniformly inside the volume

Non-uniformly inside the volume

Questions 2 of 50

Question:Two small spheres each having the charge \( + Q\) are suspended by insulating threads of length \(L\) from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be

Answers Choices:

\({180^o},\,\frac{1}{{4\pi {\varepsilon_0}}}\frac{{{Q^2}}}{{{{(2L)}^2}}}\)

\({90^o},\,\frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q^2}}}{{{L^2}}}\)

\({180^o},\,\frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q^2}}}{{2{L^2}}}\)

\({180^o},\,\frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q^2}}}{{{L^2}}}\)

Questions 3 of 50

Question:Two similar spheres having \( + \,q\) and \( - \,q\) charge are kept at a certain distance. \(F\) force acts between the two. If in the middle of two spheres, another similar sphere having \( + \,q\) charge is kept, then it experience a force in magnitude and direction as

Answers Choices:

Zero having no direction

\(8F\) towards \( + \,q\) charge

\(8F\) towards \( - \,q\) charge

\(4F\) towards \( + \,q\) charge

Questions 4 of 50

Question:A charge \(Q\) is divided into two parts of \(q\) and \(Q - q\) . If the coulomb repulsion between them when they are separated is to be maximum, the ratio of \(\frac{Q}{q}\) should be

Answers Choices:

2

\(1/2\)

4

\(1/4\)

Questions 5 of 50

Question:Two copper balls, each weighing 10g are kept in air 10 cm apart. If one electron from every \({10^6}\) atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is 63.5)

Answers Choices:

\(2.0 \times {10^{10}}\)N

\(2.0 \times {10^4}\)N

\(2.0 \times {10^8}\)N

\(2.0 \times {10^6}\)N

Questions 6 of 50

Question:Three charges each of magnitude q are placed at the corners of an equilateral triangle, the electrostatic force on the charge placed at the center is (each side of triangle is L)

Answers Choices:

Zero

\(\frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q^2}}}{{{L^2}}}\)

\(\frac{1}{{4\pi {\varepsilon _0}}}\frac{{3{q^2}}}{{{L^2}}}\)

\(\frac{1}{{12\pi {\varepsilon _0}}}\frac{{{q^2}}}{{{L^2}}}\)

Questions 7 of 50

Question:The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance \(5 \times {10^{ - 11}}m,\) will be (Charge on electron = 1.6 x 10\(^{ - 19}\) C, mass of electron = 9.1 x 10\(^{ - 31}\) kg, mass of proton = \(1.6 \times {10^{ - 27}}kg,\) \(\,G = 6.7 \times {10^{ - 11}}\,N{m^2}/k{g^2})\)

Answers Choices:

2.36 x 10\(^{39}\)

2.36 x 10\(^{40}\)

2.34 x 10\(^{41}\)

2.34 x 10\(^{42}\)

Questions 8 of 50

Question:If a unit positive charge is taken from one point to another over an equipotential surface, then

Answers Choices:

Work is done on the charge

Work is done by the charge

Work done is constant

No work is done

Questions 9 of 50

Question:The intensity of electric field required to balance a proton of mass \(1.7 \times {10^{ - 27}}kg\) and charge\(1.6 \times {10^{ - 19}}C\) is nearly

Answers Choices:

\(1 \times {10^{ - 7}}\;V/m\)

\(1 \times {10^{ - 5}}\;V/m\)

\(1 \times {10^7}\;V/m\)

\(1 \times {10^5}\;V/m\)

Questions 10 of 50

Question:At a certain distance from a point charge the electric field is \(500\,V/m\) and the potential is \(3000\,V\). What is this distance

Answers Choices:

\(6\,m\)

\(12\,m\)

\(36\,m\)

\(144\,m\)

Questions 11 of 50

Question:An alpha particle is accelerated through a potential difference of \({10^6}\,volt\). Its kinetic energy will be

Answers Choices:

\(1\,MeV\)

\(2\,MeV\)

\(4\,MeV\)

\(8\,MeV\)

Questions 12 of 50

Question:What is the potential energy of the equal positive point charges of \(1\mu C\) each held 1 m apart in air

Answers Choices:

\(9 \times {10^{ - 3}}J\)

\(9 \times {10^{ - 3}}eV\)

\(2eV/m\)

Zero

Questions 13 of 50

Question:There is a solid sphere of radius 'R' having uniformly distributed charge. What is the relation between electric field 'E' (inside the sphere) and radius of sphere 'R' is

Answers Choices:

\(E \propto {R^{ - 2}}\)

\(E \propto {R^{ - 1}}\)

\(E \propto \frac{1}{{{R^3}}}\)

\(E \propto {R^2}\)

Questions 14 of 50

Question:A particle of mass 'm' and charge 'q' is accelerated through a potential difference of V volt, its energy will be

Answers Choices:

\(qV\)

\(mqV\)

\(\left( {\frac{q}{m}} \right)V\)

\(\frac{q}{{mV}}\)

Questions 15 of 50

Question:Two point charges \( + 9e\) and \( + e\) are at 16 cm away from each other. Where should another charge q be placed between them so that the system remains in equilibrium

Answers Choices:

24 cm from \( + 9e\)

12 cm from \( + 9e\)

24 cm from \( + e\)

12 cm from \( + e\)

Questions 16 of 50

Question:A pellet carrying charge of 0.5 coulombs is accelerated through a potential of 2,000 volts. It attains a kinetic energy equal to

Answers Choices:

1000 ergs

1000 joules

1000 kWh

500 ergs

Questions 17 of 50

Question:Electric potential of earth is taken to be zero because earth is a good

Answers Choices:

Insulator

Conductor

Semiconductor

Dielectric

Questions 18 of 50

Question:In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S have positive potential and points outside S have negative potential. A positive charge, which is free to move, is placed inside S

Answers Choices:

It will remain in equilibrium

It can move inside S, but it cannot cross S

It must cross S at some time

It may move, but will ultimately return to its starting point

Questions 19 of 50

Question:The electric potential at a point on the axis of an electric dipole depends on the distance \(r\) of the point from the dipole as

Answers Choices:

\( \propto \frac{1}{r}\)

\( \propto \frac{1}{{{r^2}}}\)

\( \propto r\)

\( \propto \frac{1}{{{r^3}}}\)

Questions 20 of 50

Question:An electric dipole is placed in an electric field generated by a point charge

Answers Choices:

The net electric force on the dipole must be zero

The net electric force on the dipole may be zero

The torque on the dipole due to the field must be zero

The torque on the dipole due to the field may be zero

Questions 21 of 50

Question:Two electric dipoles of moment P and 64 P are placed in opposite direction on a line at a distance of 25 cm. The electric field will be zero at point between the dipoles whose distance from the dipole of moment P is

Answers Choices:

5 cm

\(\frac{{25}}{9}\)cm

10 cm

\(\frac{4}{{13}}\) cm

Questions 22 of 50

Question:The S.I. unit of electric flux is

Answers Choices:

Weber

Newton per coulomb

Volt x metre

Joule per coulomb

Questions 23 of 50

Question:The insulated spheres of radii \({R_1}\) and \({R_2}\) having charges \({Q_1}\)and \({Q_2}\) respectively are connected to each other. There is

Answers Choices:

No change in the energy of the system

An increase in the energy of the system

Always a decrease in the energy of the system

A decrease in the energy of the system unless \({Q_1}{R_2} = {Q_2}{R_1}\)

Questions 24 of 50

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

Answers Choices:

1000

100

10

1

Questions 25 of 50

Question:The distance between the plates of a parallel plate condenser is \(4mm\) and potential difference is\(60\;volts\). If the distance between the plates is increased to\(12mm\), then

Answers Choices:

The potential difference of the condenser will become \(180\;volts\)

The P.D. will become \(20\;volts\)

The P.D. will remain unchanged

The charge on condenser will reduce to one third

Questions 26 of 50

Question:Two metallic charged spheres whose radii are 20\(cm\) and 10\(cm\) respectively, have each 150\(micro - coulomb\) positive charge. The common potential after they are connected by a conducting wire is

Answers Choices:

\(9 \times {10^6}\;volts\)

\(4.5 \times {10^6}\;volts\)

\(1.8 \times {10^7}\;volts\)

\(13.5 \times {10^6}\;volts\)

Questions 27 of 50

Question:An air capacitor is connected to a battery. The effect of filling the space between the plates with a dielectric is to increase

Answers Choices:

The charge and the potential difference

The potential difference and the electric field

The electric field and the capacitance

The charge and the capacitance

Questions 28 of 50

Question:A parallel plate capacitor has a capacity \(C\). The separation between the plates is doubled and a dielectric medium is introduced between the plates. If the capacity now becomes\(2C\), the dielectric constant of the medium is

Answers Choices:

2

1

4

8

Questions 29 of 50

Question:The force between the plates of a parallel plate capacitor of capacitance\(C\) and distance of separation of the plates \(d\) with a potential difference \(V\) between the plates, is

Answers Choices:

\(\frac{{C{V^2}}}{{2d}}\)

\(\frac{{{C^2}{V^2}}}{{2{d^2}}}\)

\(\frac{{{C^2}{V^2}}}{{{d^2}}}\)

\(\frac{{{V^2}d}}{C}\)

Questions 30 of 50

Question:Two metal spheres of capacitance \({C_1}\) and \({C_2}\) carry some charges. They are put in contact and then separated. The final charges \({Q_1}\) and \({Q_2}\) on them will satisfy

Answers Choices:

\(\frac{{{Q_1}}}{{{Q_2}}} < \frac{{{C_1}}}{{{C_2}}}\)

\(\frac{{{Q_1}}}{{{Q_2}}} = \frac{{{C_1}}}{{{C_2}}}\)

\(\frac{{{Q_1}}}{{{Q_2}}} > \frac{{{C_1}}}{{{C_2}}}\)

\(\frac{{{Q_1}}}{{{Q_2}}} < \frac{{{C_2}}}{{{C_1}}}\)

Questions 31 of 50

Question:When a dielectric material is introduced between the plates of a charged condenser then electric field between the plates

Answers Choices:

Decreases

Increases

Remain constant

First

Questions 32 of 50

Question:A parallel plate capacitor has a plate separation of 0.01 mm and use a dielectric (whose dielectric strength is 19 KV/mm) as an insulator. The maximum potential difference that can be applied to the terminals of the capacitor is

Answers Choices:

190 V

290 V

95 V

350 V

Questions 33 of 50

Question:The capacity of the conductor does not depend upon

Answers Choices:

Charge

Voltage

Nature of the material

All of these

Questions 34 of 50

Question:A solid conducting sphere of radius \({R_1}\) is surrounded by another concentric hollow conducting sphere of radius \({R_2}\). The capacitance of this assembly is proportional to

Answers Choices:

\(\frac{{{R_2} - {R_1}}}{{{R_1}{R_2}}}\)

\(\frac{{{R_2} + {R_1}}}{{{R_1}{R_2}}}\)

\(\frac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}\)

\(\frac{{{R_1}{R_2}}}{{{R_2} - {R_1}}}\)

Questions 35 of 50

Question:A conducting sphere of radius 10cm is charged \(10\mu \,C\). Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that if the sphere are separated, then surface density of charges, on the spheres will be in the ratio of

Answers Choices:

1:04

1:03

2:01

1:01

Questions 36 of 50

Question:64 small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is

Answers Choices:

0.086

64:01:00

4:01

1:04

Questions 37 of 50

Question:A capacitor is charged to 200 volt it has 0.1 coulomb charge. When it is discharged, energy will be

Answers Choices:

1 J

4 J

10 J

20 J

Questions 38 of 50

Question:If eight identical drops are joined to form a bigger drop, the potential on bigger as compared to that on smaller drop will be

Answers Choices:

Double

Four times

Eight times

One time

Questions 39 of 50

Question:The potentials of the two plates of capacitor are +10V and -10 V. The charge on one of the plates is 40 C. The capacitance of the capacitor is

Answers Choices:

2 F

4 F

0.5 F

0.25 F

Questions 40 of 50

Question:The potential to which a conductor is raised, depends on

Answers Choices:

The amount of charge

Geometry and size of the conductor

Both 1 and 2

Only on

Questions 41 of 50

Question:Two capacitors connected in parallel having the capacities \({C_1}\)and \({C_2}\) are given \('q'\) charge, which is distributed among them. The ratio of the charge on \({C_1}\)and \({C_2}\) will be

Answers Choices:

\(\frac{{{C_1}}}{{{C_2}}}\)

\(\frac{{{C_2}}}{{{C_1}}}\)

\({C_1}{C_2}\)

\(\frac{1}{{{C_1}{C_2}}}\)

Questions 42 of 50

Question:Two capacitors of capacities \({C_1}\) and \({C_2}\) are charged to voltages \({V_1}\) and \({V_2}\) respectively. There will be no exchange of energy in connecting them in parallel, if

Answers Choices:

\({C_1} = {C_2}\)

\({C_1}{V_1} = {C_2}{V_2}\)

\({V_1} = {V_2}\)

\(\frac{{{C_1}}}{{{V_1}}} = \frac{{{C_2}}}{{{V_2}}}\)

Questions 43 of 50

Question:Two capacitors of 3pF and 6pF are connected in series and a potential difference of 5000\(V\) is applied across the combination. They are then disconnected and reconnected in parallel. The potential between the plates is

Answers Choices:

2250\(V\)

2222\(V\)

\(2.25 \times {10^6}V\)

\(1.1 \times {10^6}V\)

Questions 44 of 50

Question:Two identical parallel plate capacitors are connected in series to a battery of 100\(V\). A dielectric slab of dielectric constant 4.0 is inserted between the plates of second capacitor. The potential difference across the capacitors will now be respectively

Answers Choices:

50 V, 50 V

80 V, 20 V

20 V, 80 V

75 V, 25 V

Questions 45 of 50

Question:Three capacitors of capacitance \(3\mu \,F,\,10\mu \,F\,\) and \(15\mu \,F\,\) are connected in series to a voltage source of 100V. The charge on \(15\mu \,F\,\)is

Answers Choices:

\(50\,\mu \,C\)

\(100\,\mu \,C\)

\(200\,\mu \,C\)

\(280\,\mu \,C\)

Questions 46 of 50

Question:A 20F capacitor is charged to 5V and isolated. It is then connected in parallel with an uncharged 30F capacitor. The decrease in the energy of the system will be

Answers Choices:

25 J

200 J

125 J

150 J

Questions 47 of 50

Question:A 10 \(\mu \)F capacitor is charged to a potential difference of 1000 V. The terminals of the charged capacitor are disconnected from the power supply and connected to the terminals of an uncharged 6\(\mu \)F capacitor. What is the final potential difference across each capacitor

Answers Choices:

167 V

100 V

625 V

250 V

Questions 48 of 50

Question:In the given circuit if point C is connected to the earth and a potential of \( + \,2000\,V\) is given to the point A, the potential at B is

Answers Choices:

\(1500\,V\)

\(1000\;V\)

\(500\;V\)

\(400\;V\)

Questions 49 of 50

Question:Figure shows two capacitors connected in series and joined to a battery. The graph in figure shows the variation in potential as one moves from left to right on the branch containing the capacitors, if

Answers Choices:

\({C_1} > {C_2}\)

\({C_1} = {C_2}\)

\({C_1} < {C_2}\)

The information is not sufficient to decide the relation between \({C_1}\)and \({C_2}\)

Questions 50 of 50

Question:During charging a capacitor variation of potential V of the capacitor with time t is shown as

Answers Choices: