# Electrostatics Test 4

Total Questions:50 Total Time: 75 Min

Remaining:

## Questions 1 of 50

Question:A body can be negatively charged by

Giving excess of electrons to it

Removing some electrons from it

Giving some protons to it

Removing some neutrons from it

## Questions 2 of 50

Question:Force of attraction between two point charges $$Q$$ and – Q separated by $$d\,metre$$ is $${F_e}$$ . When these charges are placed on two identical spheres of radius $$R = 0.3\,d$$ whose centres are $$d\,metre$$ apart, the force of attraction between them is

Greater than $${F_e}$$

Equal to $${F_e}$$

Less than $${F_e}$$

Less than $${F_e}$$

## Questions 3 of 50

Question:Charge on $$\alpha$$ -particle is

$$4.8 \times {10^{ - 19}}C$$

$$1.6 \times {10^{ - 19}}C$$

$$3.2 \times {10^{ - 19}}C$$

$$6.4 \times {10^{ - 19}}C$$

## Questions 4 of 50

Question:Equal charges $$q$$ are placed at the four corners $$A,\,B,\,C,\,D$$ of a square of length $$a$$. The magnitude of the force on the charge at B will be

$$\frac{{3{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$$

$$\frac{{4{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$$

$$\left( {\frac{{1 + 2\sqrt 2 }}{2}} \right)\frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$$

$$\left( {2 + \frac{1}{{\sqrt 2 }}} \right)\frac{{{q^2}}}{{4\pi {\varepsilon _0}{a^2}}}$$

## Questions 5 of 50

Question:The electric charge in uniform motion produces

An electric field only

A magnetic field only

Both electric and magnetic field

Neither electric nor magnetic field

## Questions 6 of 50

Question:The distance between the two charges $$25\mu C$$ and $$36\mu C$$ is $$11cm$$ At what point on the line joining the two, the intensity will be zero

At a distance of $$5\,cm$$from $$25\mu C$$

At a distance of $$5\,cm$$from $$36\mu C$$

At a distance of $$10\,cm$$from $$25\mu C$$

At a distance of $$11\,cm$$from $$36\mu C$$

## Questions 7 of 50

Question:Two spheres $$A$$and $$B$$ of radius $$4cm$$ and $$6cm$$ are given charges of $$80\mu c$$ and $$40\mu c$$respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is

$$20\mu C$$from $$A$$to $$B$$

$$16\mu C$$ from $$A$$to $$B$$

$$32\mu C$$from $$B$$ to $$A$$

$$32\mu C$$ from $$A$$to $$B$$

## Questions 8 of 50

Question:Four equal charges $$Q$$ are placed at the four corners of a square of each side is $$'a'$$. Work done in removing a charge -Q from its centre to infinity is

0

$$\frac{{\sqrt 2 {Q^2}}}{{4\pi {\varepsilon _0}a}}$$

$$\frac{{\sqrt 2 {Q^2}}}{{\pi {\varepsilon _0}a}}$$

$$\frac{{{Q^2}}}{{2\pi {\varepsilon _0}a}}$$

## Questions 9 of 50

Question:A particle $$A$$ has charge $$+ q$$ and a particle $$B$$ has charge $$+ \,4q$$ with each of them having the same mass $$m$$. When allowed to fall from rest through the same electric potential difference, the ratio of their speed $$\frac{{{v_A}}}{{{v_B}}}$$ will become

$$2:1$$

$$1:2$$

$$1:4$$

$$4:1$$

## Questions 10 of 50

Question:Two insulated charged conducting spheres of radii $$20\,cm$$ and $$15\,cm$$respectively and having an equal charge of $$10\,C$$ are connected by a copper wire and then they are separated. Then

Both the spheres will have the same charge of $$10\,C$$

Surface charge density on the $$20\,cm$$ sphere will be greater than that on the $$15\,cm$$ sphere

Surface charge density on the $$15\,cm$$sphere will be greater than that on the $$20\,cm$$ sphere

Surface charge density on the two spheres will be equal

## Questions 11 of 50

Question:Equal charges $$q$$ are placed at the vertices $$A$$ and $$B$$ of an equilateral triangle $$ABC$$ of side $$a$$. The magnitude of electric field at the point $$C$$ is

$$\frac{q}{{4\pi {\varepsilon _0}{a^2}}}$$

$$\frac{{\sqrt 2 \,q}}{{4\pi {\varepsilon _0}{a^2}}}$$

$$\frac{{\sqrt 3 \,q}}{{4\pi {\varepsilon _0}{a^2}}}$$

$$\frac{q}{{2\pi {\varepsilon _0}{a^2}}}$$

## Questions 12 of 50

Question:A sphere of radius $$1\,cm$$ has potential of $$8000\,V$$, then energy density near its surface will be

$$64 \times {10^5}J/{m^3}$$

$$8 \times {10^3}J/{m^3}$$

$$32\,J/{m^3}$$

$$2.83\,J/{m^3}$$

## Questions 13 of 50

Question:Point charges $$+ 4q,\, - q$$ and $$+ 4q$$ are kept on the $$x -$$axis at points $$x = 0,\,x = a$$ and $$x = 2a$$ respectively, then

Only $$q$$ is in stable equilibrium

None of the charges are in equilibrium

All the charges are in unstable equilibrium

All the charges are in stable equilibrium

## Questions 14 of 50

Question:Two charges of $$4\mu C$$ each are placed at the corners A and B of an equilateral triangle of side length 0.2 m in air. The electric potential at C is $$\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\frac{{N{\rm{ - }}{m^2}}}{{{C^2}}}} \right]$$

$$9 \times {10^4}$$V

$$18 \times {10^4}$$V

$$36 \times {10^4}$$V

$$36 \times {10^{ - 4}}$$V

## Questions 15 of 50

Question:Electric field strength due to a point charge of $$5\mu C$$ at a distance of 80 cm from the charge is

$$8 \times {10^4}$$N/C

$$7 \times {10^4}$$N/C

$$5 \times {10^4}$$N/C

$$4 \times {10^4}$$N/C

## Questions 16 of 50

Question:The dimension of (1/2) $${\varepsilon _0}{E^2}({\varepsilon _0}$$: permittivity of free space; $$E$$: electric field) is

$$ML{T^{^{ - 1}}}$$

$$M{L^2}{T^{ - 2}}$$

$$M{L^{ - 1}}{T^{ - 2}}$$

$$M{L^2}{T^{ - 1}}$$

## Questions 17 of 50

Question:A cube of a metal is given a positive charge Q. For the above system, which of the following statements is true

Electric potential at the surface of the cube is zero

Electric potential within the cube is zero

Electric field is normal to the surface of the cube

Electric field varies within the cube

## Questions 18 of 50

Question:The work done in bringing a 20 coulomb charge from point A to point B for distance 0.2m is 2J. The potential difference between the two points will be (in volt)

0.2

8

0.1

0.4

## Questions 19 of 50

Question:A hollow sphere of charge does not produce an electric field at any

Point beyond 2 metres

Point beyond 10 metres

Interior point

Outer point

## Questions 20 of 50

Question:A conducting sphere of radius $$R = 20$$cm is given a charge $$Q = 16\mu C$$. What is $$\overrightarrow E$$ at centre

$$3.6 \times {10^6}N/C$$

$$1.8 \times {10^6}N/C$$

Zero

$$0.9 \times {10^6}N/C$$

## Questions 21 of 50

Question: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 a distance $$\frac{R}{2}$$ from the centre of the shell is

$$\frac{{(q + Q)}}{{4\pi {\varepsilon _0}}}\frac{2}{R}$$

$$\frac{{2Q}}{{4\pi {\varepsilon _0}R}}$$

$$\frac{{2Q}}{{4\pi {\varepsilon _0}R}} - \frac{{2q}}{{4\pi {\varepsilon _0}R}}$$

## Questions 22 of 50

Question:When a negative charge is taken at a height from earth's surface, then its potential energy

Decreases

Increases

Remains unchanged

Will become infinity

## Questions 23 of 50

Question:When a charge of 3 coulombs is placed in a uniform electric field, it experiences a force of 3000 Newton. Within this field, potential difference between two points separated by a distance of 1 cm is

10 volts

90 volts

1000 volts

3000 volts

## Questions 24 of 50

Question:The potential at a distance R/2 from the centre of a conducting sphere of radius R will be

0

$$\frac{Q}{{8\pi {\varepsilon _0}R}}$$

$$\frac{Q}{{4\pi {\varepsilon _0}R}}$$

$$\frac{Q}{{2\pi {\varepsilon _0}R}}$$

## Questions 25 of 50

Question:Four charges $$+ Q,\, - Q,\, + Q,\, - Q$$ are placed at the corners of a square taken in order. At the centre of the square

$$E = 0,\,V = 0$$

$$E = 0,\,V \ne 0$$

$$E \ne 0,\,V = 0$$

$$E = 0,\,V \ne 0$$

## Questions 26 of 50

Question:At a point 20 cm from the centre of a uniformly charged dielectric sphere of radius 10 cm, the electric field is 100 V/m. The electric field at 3 cm from the centre of the sphere will be

150 V/m

125 V/m

120 V/m

Zero

## Questions 27 of 50

Question:Charges 4Q, q and Q and placed along x-axis at positions $$x = 0,x = l/2$$ and $$x = l$$, respectively. Find the value of q so that force on charge Q is zero

Q

Q / 2

Q / 2

Q

## Questions 28 of 50

Question: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 $$\frac{\pi }{3}$$ with the x-axis. If the electric field at $$P$$ makes an angle $$\theta$$ with the x-axis, the value of $$\theta$$ would be

$$\frac{\pi }{3}$$

$$\frac{\pi }{3} + {\tan ^{ - 1}}\left( {\frac{{\sqrt 3 }}{2}} \right)$$

$$\frac{{2\pi }}{3}$$

$${\tan ^{ - 1}}\left( {\frac{{\sqrt 3 }}{2}} \right)$$

## Questions 29 of 50

Question:Electric charges $$q,\,q,\, - 2q$$ are placed at the corners of an equilateral triangle $$ABC$$ of side $$l$$. The magnitude of electric dipole moment of the system is

$$ql$$

$$2ql$$

$$\sqrt 3 ql$$

$$4ql$$

## Questions 30 of 50

Question:Intensity of an electric field E due to a dipole, depends on distance r as

$$E \propto \frac{1}{{{r^4}}}$$

$$E \propto \frac{1}{{{r^3}}}$$

$$E \propto \frac{1}{{{r^2}}}$$

$$E \propto \frac{1}{r}$$

## Questions 31 of 50

Question:The ratio of electric fields on the axis and at equator of an electric dipole will be

1:01

2:01

4:01

None of these

## Questions 32 of 50

Question:A cube of side $$l$$ is placed in a uniform field E, where$$E = E\hat i$$. The net electric flux through the cube is

Zero

$${l^2}E$$

$$4{l^2}E$$

$$6{l^2}E$$

## Questions 33 of 50

Question:The electric intensity due to an infinite cylinder of radius $$R$$ and having charge q per unit length at a distance $$r(r > R)$$from its axis is

Directly proportional to $${r^2}$$

Directly proportional to $${r^3}$$

Inversely proportional to r

Inversely proportional to $${r^2}$$

## Questions 34 of 50

Question:Separation between the plates of a parallel plate capacitor is $$d$$and the area of each plate is $$A$$. When a slab of material of dielectric constant$$k$$and thickness $$t(t < d)$$ is introduced between the plates, its capacitance becomes

$$\frac{{{\varepsilon _0}A}}{{d + t\left( {1 - \frac{1}{k}} \right)}}$$

$$\frac{{{\varepsilon _0}A}}{{d + t\left( {1 + \frac{1}{k}} \right)}}$$

$$\frac{{{\varepsilon _0}A}}{{d - t\left( {1 - \frac{1}{k}} \right)}}$$

$$\frac{{{\varepsilon _0}A}}{{d - t\left( {1 + \frac{1}{k}} \right)}}$$

## Questions 35 of 50

Question:The area of each plate of a parallel plate capacitor is $$100\,c{m^2}$$and the distance between the plates is$$1mm$$. It is filled with mica of dielectric 6. The radius of the equivalent capacity of the sphere will be

$$47.7\;m$$

4.77 $$m$$

477 $$m$$

None of the above

## Questions 36 of 50

Question:One plate of parallel plate capacitor is smaller than other, then charge on smaller plate will be

Less than other

More than other

Equal to other

Will depend upon the medium between them

## Questions 37 of 50

Question:The electric field between the two spheres of a charged spherical condenser

Is zero

Is constant

Increases with distance from the centre

Decreases with distance from the centre

## Questions 38 of 50

Question:Two spherical conductors each of capacity $$C$$ are charged to potentials $$V$$ and $$- V$$. These are then connected by means of a fine wire. The loss of energy will be

Zero

$$\frac{1}{2}C{V^2}$$

$$C{V^2}$$

$$2C{V^2}$$

## Questions 39 of 50

Question:The ratio of charge to potential of a body is known as

Capacitance

Conductance

Inductance

Resistance

## Questions 40 of 50

Question:Two insulated metallic spheres of $$3\mu F$$ and $$5\mu F$$ capacitances are charged to 300 V and 500V respectively. The energy loss, when they are connected by a wire is

0.012 J

0.0218 J

0.0375 J

3.75 J

## Questions 41 of 50

Question:If the distance between parallel plates of a capacitor is halved and dielectric constant is doubled then the capacitance

Decreases two times

Increases two times

Increases four times

Remain the same

## Questions 42 of 50

Question:The work done in placing a charge of $$8 \times {10^{ - 18}}$$ coulomb on a condenser of capacity 100 micro-farad is

$$32 \times {10^{ - 32}}\,Joule$$

$$16 \times {10^{ - 32}}\,Joule$$

$$3.1 \times {10^{ - 26}}\,Joule$$

$$4 \times {10^{ - 10}}\,Joule$$

## Questions 43 of 50

Question:A 4 $$\mu$$F condenser is charged to 400 V and then its plates are joined through a resistance. The heat produced in the resistance is

0.16 J

0.32 J

0.64 J

1.28 J

## Questions 44 of 50

Question:The capacitor of capacitance $$4\mu F$$ and$$6\mu F$$ are connected in series. A potential difference of $$500\;volts$$ is applied to the outer plates of the two capacitor system. The potential difference across the plates of capacitor of $$4\mu F$$ capacitance is

$$500\;volts$$

$$300\;volts$$

$$200\;volts$$

$$250\;volts$$

## Questions 45 of 50

Question:A condenser having a capacity of 6$$\mu$$F is charged to 100 V and is then joined to an uncharged condenser of $$14\mu F$$ and then removed. The ratio of the charges on 6$$\mu$$F and 14$$\mu$$F and the potential of 6$$\mu$$F will be

$$\frac{6}{{14}}$$ and $$50\;volt$$

$$\frac{{14}}{6}$$ and $$30\;volt$$

$$\frac{6}{{14}}$$ and $$30\;volt$$

$$\frac{{14}}{6}$$ and 0$$volt$$

## Questions 46 of 50

Question:A capacitor of $$20\mu F$$ is charged to $$500\;volts$$ and connected in parallel with another capacitor of $$10\mu F$$and charged to $$200\;volts$$. The common potential is

$$200\;volts$$

$$300\;volts$$

$${\rm{400 }}volts$$

$${\rm{500 }}volts$$

## Questions 47 of 50

Question:A capacitor of capacity $${C_1}$$is charged upto V volt and then connected to an uncharged capacitor of capacity $${C_2}$$. Then final potential difference across each will be

$$\frac{{{C_2}V}}{{{C_1} + {C_2}}}$$

$$\left( {1 + \frac{{{C_2}}}{{{C_1}}}} \right)\,V$$

$$\frac{{{C_1}V}}{{{C_1} + {C_2}}}$$

$$\left( {1 - \frac{{{C_2}}}{{{C_1}}}} \right)\,V$$

## Questions 48 of 50

Question:A charged particle q is shot towards another charged particle Q which is fixed, with a speed $$\nu$$. It approaches Q upto a closest distance r and then returns. If q were given a speed $$2\nu$$, the closest distances of approach would be

r

2r

r/2

r/4

## Questions 49 of 50

Question:The figure gives the electric potential V as a function of distance through five regions on $$x$$-axis. Which of the following is true for the electric field E in these regions

$${E_1} > {E_2} > {E_3} > {E_4} > {E_5}$$

$${E_1} = {E_3} = {E_5}$$ and $${E_2} < {E_4}$$

$${E_2} = {E_4} = {E_5}$$ and $${E_1} < {E_3}$$

$${E_1} < {E_2} < {E_3} < {E_4} < {E_5}$$

## Questions 50 of 50

Question:Which of the following graphs shows the variation of electric field E due to a hollow spherical conductor of radius R as a function of distance from the centre of the sphere