Charge and Force MCQs

Question 1

Two charges, each of charge 1 μC, are separated by a distance of 1 m. The electrostatic force between the two charges is:

Accepted Answer

9 × 10⁻³ N

Answer

9 × 10⁹ N

Answer

9 × 10³ N

Answer

9 × 10⁻⁶ N

Question 2

Number of electrons required to produce one coulomb charge is:

Accepted Answer

$6.25\times10^{18}$

Answer

$6.023\times10^{23}$

Answer

$1.6\times10^{-19}$

Answer

$6.25\times10^{-8}$

Question 3

Force between two identical sphere carrying charges +10 μC and −20 μC, kept at certain distance is F. If these two spheres are made in contact and then separated to the distance, force is F'. The ratio of these two forces is:

Accepted Answer

−8:1

Answer

8:1

Answer

16:1

Answer

−16:1

Question 4

A positively charged particle moving east enters a region of uniform magnetic field directed vertically upwards. The particle will:

Accepted Answer

Move in a circular orbit with constant speed

Answer

Deflect vertically upwards

Answer

Move in a circular orbit with increased speed

Answer

Continue moving east

Question 5

A moving charged particle experiences force in:

Accepted Answer

A magnetic field when velocity has a component perpendicular to the field

Answer

Only an electric field, never a magnetic field

Answer

Any magnetic field, even when velocity is parallel to it

Answer

No force in an electric field

Question 6

Two ebonite rods A and B of radii 1.5cm and 2cm rubbed together will:

Accepted Answer

Both remain neutral

Answer

A becomes positively charged

Answer

A becomes negatively charged

Answer

Both acquire similar charges

Question 7

A thin water stream from tap is attracted by a rod placed near it. The rod is:

Accepted Answer

Charged with static electricity

Answer

South pole of magnet

Answer

North pole of magnet

Answer

Non-magnetic substance

Question 8

Neutral metal gains 32μC charge when rubbed with wool. Electron transfer count:

Accepted Answer

$2\times 10^{14}$

Answer

$1.25\times 10^{11}$

Answer

$2.5\times 10^{12}$

Answer

$5\times 10^{13}$

Question 9

Force between electron and proton at 0.53Å separation:

Accepted Answer

$8.2\times10^{-8}\,\mathrm N$

Answer

$8.2\times10^{-4}\,\mathrm N$

Answer

$8.2\times10^{-5}\,\mathrm N$

Answer

$8.2\times10^{-3}\,\mathrm N$

Question 10

Ratio of electric to gravitational force between electrons:

Accepted Answer

$10^{42}$

Answer

$10^{39}$

Answer

$10^{36}$

Answer

$10^{9}$

Question 11

Force between two 1μC charges at 1m separation:

Accepted Answer

$9\times 10^{-3}\,\mathrm N$

Answer

$9\times 10^{-4}\,\mathrm N$

Answer

$9\times 10^{-5}\,\mathrm N$

Answer

$9\times 10^{-2}\,\mathrm N$

Question 12

Positive charge Q released between two fixed -q charges at (0,a) and (0,-a): Two equal negative charged —q are fixed at the points (0, a) & (0, —a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on x-axis. The charge Q will

Accepted Answer

Oscillates non-SHM

Answer

Moves to infinity

Answer

Stops at origin

Answer

Executes SHM

Question 13

Glass rod becomes positive when rubbed with silk due to:

Accepted Answer

Electron removal

Answer

Electron addition

Answer

Proton addition

Answer

Proton removal

Question 14

Work done moving charge on equipotential surface:

Accepted Answer

Zero

Answer

$q/(4\pi \varepsilon _{0}r)$

Answer

$q^{2}/(4\pi \varepsilon _{0}r)$

Answer

$q^{2}/r$

Question 15

Specific charge of electron:

Accepted Answer

$1.76\times 10^{11}\,\mathrm{C/kg}$

Answer

$1.76\times 10^{-11}\,\mathrm{C/kg}$

Answer

$6.023\times 10^{-23} C$

Answer

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

Question 16

Charged sphere (radius a, charge Q) contacts uncharged sphere (radius b). Remaining charge on A:

Accepted Answer

$\frac{aQ}{a+b}$

Answer

$aQ/b$

Answer

$bQ/a$

Answer

$\frac{bQ}{a+b}$

Question 17

Distance between plates with E=10 6 V/m and ΔV=10 3 V:

Accepted Answer

$10^{-3}\,\mathrm m$

Answer

$10^{9}\,\mathrm m$

Answer

$10^{15}\,\mathrm m$

Answer

$10^{39}\,\mathrm m$

Question 18

Equipotential surface for point charge at large distance appears:

Accepted Answer

Spherical

Answer

Plane

Answer

Circular

Answer

Elliptical

Question 19

If the potentil of metallic sphere 100V with respect to far away. Calculate the surface charge density if the radius of sphere 2cm.

Accepted Answer

$4.4\times10^{-8}\,\mathrm{C/m^2}$

Answer

$4.4\times10^{-7}\,\mathrm{C/m^2}$

Answer

$2.4\times10^{-6}\,\mathrm{C/m^2}$

Answer

$2.4\times10^{-5}\,\mathrm{C/m^2}$

Question 20

Identical charges are kept at each corner of a cube of length a. The net potential at the center of cube is

Accepted Answer

$4q/(\sqrt 3\pi \varepsilon _{0}a)$

Answer

$2q/(\sqrt 3\pi \varepsilon _{0}a)$

Answer

$\sqrt 3q/(\pi \varepsilon _{0}a)$

Answer

Zero

Question 21

Correct statement about matter waves:

Accepted Answer

All moving particles have matter waves

Answer

Only charged particles have matter waves

Answer

Only subatomic particles have matter waves

Answer

No particles have matter waves

Question 22

On penetrating a uniformly charged sphere, the electrical field strength E

Accepted Answer

Increases

Answer

Constant

Answer

Decreases

Answer

Zero

Question 23

Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1,2), (2, 4), (4,1) show electrostatic attraction, while pairs (2,3) and (4,5) show repulsion. Therefore, ball 1 must be

Accepted Answer

Neutral

Answer

Positive

Answer

Negative

Answer

Metallic

Question 24

Characteristic of electric field lines:

Accepted Answer

The tangent to a field line gives the direction of the electric field

Answer

They always point from negative to positive

Answer

Their density decreases where the field is stronger

Answer

They are physical threads in space

Question 25

Two concentric spheres are carrying a charge Q and q. When the two spheres are joined by a wire, the charge on the outer surface of the inner sphere is

Accepted Answer

Zero

Answer

Q-q

Answer

Q

Answer

Q+q

Question 26

When two bodies are rubbed against each other they are electrified. Which one of the followin is correct?

Accepted Answer

Glass becomes +ve with ebonite

Answer

Glass becomes -ve with metal

Answer

Glass becomes +ve with flannel

Answer

Glass becomes -ve with amber

Question 27

Divergence of gold leaf is used to study

Accepted Answer

Charge

Answer

Potential

Answer

Energy

Answer

None

Question 28

When a woolen sweater worm over a nylon shirt is removed, sparking is observed due to

Accepted Answer

Static electricity

Answer

Current electricity

Answer

None

Answer

Both

Question 29

A charge q is placed at the centre of the line joining two equal charges Q. The system of three charges will be in equilibrium if q is equal to:

Accepted Answer

$-Q/4$

Answer

$-Q/2$

Answer

$-4Q$

Answer

$Q/2$

Question 30

Where a charge Q is kept between +q and +nq (n > 0) so that net force experienced by +Q charge will be zero. Assume distance between charges is r

Accepted Answer

$\frac{r}{1+\sqrt n}\;\text{from }+q$

Answer

$\frac{r}{1+1/\sqrt n}\;\text{from }+q$

Answer

$\frac{r^2}{1+1/\sqrt n}\;\text{from }+q$

Answer

$\frac{r}{\sqrt{1+n}}\;\text{from }+q$

Question 31

Force between two identical spheres carrying charge +10μC and -20μC, kept at certain distance is F. If these two spheres are made in contact and then separated to the distance, force is F'. The ratio of these two force is

Accepted Answer

$-8:1$

Answer

$8:1$

Answer

$16:1$

Answer

$-16:1$

Question 32

A charge Q = 120μC is to be divided into two parts q and Q—q. These parts are kept at certain distance then for what value Of q the force between them will be maximum?

Accepted Answer

$60\,\mu\mathrm C$

Answer

$40\,\mu\mathrm C$

Answer

$30\,\mu\mathrm C$

Answer

$10\,\mu\mathrm C$

Question 33

The distance between two. charges is increased by 25% then the percentage change in force is

Accepted Answer

36% decrease

Answer

56% decrease

Answer

65% decrease

Answer

50% decrease

Question 34

Coloumb force between two charges kept at certain distance is F. If 'half of separåtion between them is filled with dielectric of constant ε r = 4, then the new Coloumb's force is

Accepted Answer

$4F/9$

Answer

$F$

Answer

$3F/8$

Answer

$2F/9$

Question 35

There are two charges +1μC and +3μC. The ratio of the forces acting on them will be

Accepted Answer

$1:1$

Answer

$1:3$

Answer

$3:1$

Answer

$1:25$

Question 36

A charge q 1 exerts some force on a second charge q 2 . If third charge q 3 is brought near, the force q 1 exerted on q 2 :

Accepted Answer

Remains same

Answer

Increases

Answer

Decreases

Answer

Depends on signs

Question 37

Two equally charged identical metal spheres A and B repel each other with a force 3×10 -5 N. Another identical unchanged sphere C is touched with A and then placed at the mid-point between A and B. Net force on C is(initial force ):

Accepted Answer

$3\times 10^{-5}\,\mathrm N$

Answer

$1\times 10^{-5}\,\mathrm N$

Answer

$2\times 10^{-5}\,\mathrm N$

Answer

$1.5\times 10^{-5}\,\mathrm N$

Question 38

A polythene piece, rubbed with wool is found to have negative charge of 4×10 -7 C. The number of electrons transferred from wool to polythene is

Accepted Answer

$2.5\times 10^{12}$

Answer

$1.5\times 10^{12}$

Answer

$2.5\times 10^{13}$

Answer

$3.5\times 10^{13}$

Question 39

Two insulated metal spheres of radii 10cm and 15cm charged .to a potential of 150V and respectively are connected by means of a metallic wire. What is ihe charge on the first sphere?

Accepted Answer

Cannot be determined: the second sphere’s initial potential is missing

Answer

$2\,\mathrm{esu}$

Answer

$6\,\mathrm{esu}$

Answer

$4\,\mathrm{esu}$

Question 40

Two identical Α and Β are supported on insulating stands and placed in contact. What kind of charges will Α and Β develop when a negatively charged ebonite rod is brought near Α?

Accepted Answer

A: +ve, B: -ve

Answer

A: -ve, B: +ve

Answer

Both +ve

Answer

Both -ve

Charge	Meaning	Mass effect
Positive charge	Deficiency/loss of electrons	Mass slightly decreases
Negative charge	Excess/gain of electrons	Mass slightly increases

Charges	Force
Like charges	Repel
Unlike charges	Attract
Sure test of electrification	Repulsion

Condition of charge	Produces
Charge at rest	Electric field only
Charge in uniform/unaccelerated motion	Electric field + magnetic field
Accelerated charge	Electric field + magnetic field + electromagnetic radiation

Method	Meaning
Friction	Charging by rubbing
Conduction	Charging by contact
Induction	Charging without contact

Body / Medium	\(\epsilon_r\)	Induced charge
Air / vacuum	1	\(q_{induced}=0\)
Insulator	>1	Magnitude less than inducing charge
Conductor	\(\infty\)	\(q_{induced}=-q_{inducing}\)

34Charge and Force

Table 1: Positive and Negative Charge

Table 1: Interaction of Charges

Table 1: Charge Motion and Fields

Table 1: Methods of Charging

Table 1: Induced Charge in Different Media

Table 1: Charge Density

Table 1: Coulomb Force Formulae

Table 2: Constants

Table 1: Important Unit Relations

Table 1: Charge Sharing

Table 1: Types of Dielectrics

Table 1: Nature of Forces

Table 1: Useful Results

Table 1: Two Identical Charged Pith Balls

Table 1: Charge Equilibrium Configurations

Table 1: Position Where Third Charge Experiences Zero Force

Table 1: Gold Leaf Electroscope Test

Table 1: Examples

Table 1: Important Points

Table 1: Charge and Force One-Liners

More CEE preparation resources

Type	Symbol	Formula
Linear charge density	\(\lambda\)	\(\lambda=\frac{q}{l}\)
Surface charge density	\(\sigma\)	\(\sigma=\frac{q}{A}\)
Volume charge density	\(\rho\)	\(\rho=\frac{q}{V}\)

Condition	Formula
In air/vacuum
Using constant	\(F=9\times10^9\frac{q_1q_2}{r^2}\)
In medium
In dielectric medium
Relative permittivity

Quantity	Value / Meaning
\(\frac{1}{4\pi\epsilon_0}\)	\(9\times10^9\ Nm^2C^{-2}\)
\(\epsilon_0\)	\(8.85\times10^{-12}\ C^2N^{-1}m^{-2}\)
\(\epsilon_0\)	Permittivity of free space
\(\epsilon_r\)	Relative permittivity / dielectric constant
\(\epsilon_r\)	No unit and no dimension

Quantity	Relation
1 coulomb	\(6.25\times10^{18}\) electrons
CGS unit of charge	esu / stat coulomb
1 coulomb	\(3\times10^9\ esu\)
1 volt	\(\frac{1}{300}\ statvolt\)
1 farad	\(9\times10^{11}\ statfarad\)

Initial charges	Final charge on each conductor
\(q_1\) and \(q_2\)	\(\frac{q_1+q_2}{2}\)
\(q_1\) and \(-q_2\)	\(\frac{q_1-q_2}{2}\)

Type	Examples	Description
Non-polar dielectrics	\(N_2,O_2\), benzene, methane	Centre of positive charge coincides with centre of negative charge
Polar dielectrics	\(H_2O,CO_2,NH_3,HCl\)	Centre of positive charge does not coincide with centre of negative charge

Force	Nature
Coulomb force	Attractive or repulsive
Gravitational force	Always attractive
Coulomb force	Depends on medium
Gravitational force	Independent of medium
Order of strength	\(F_{nuclear}>F_C>F_G\)

Condition	Result
One charge very large compared to another	Even like charges may attract due to induction
	Each part = \(\frac{Q}{2}\)
Two small spheres with constant charge: force in air : force in medium	\(K:1\)
Two small spheres at constant potential: force in air : force in medium	\(1:K\)

Condition	Formula / Result

In gravity-free space	Angle between strings = \(180^\circ\)
Tension in each string in gravity-free space
In liquid, same distance remains	\(K=\frac{\sigma}{\sigma-\rho}\)

Configuration	Charge required for equilibrium
	\(Q=-\frac{q}{\sqrt3}\)
If \(Q=-q\) at centroid	All three corner charges move to centroid
	\(Q=-\frac{q}{4}(1+2\sqrt2)\)
	\(q=-\frac{Q}{4}\)

Observation	Conclusion
Leaves do not diverge	Body is uncharged
Leaves diverge	Body is charged

Given charges	Zero force position
Like charges	Between the charges, nearer to lower magnitude charge
Unlike charges	Outside the charges, nearer to lower magnitude charge
Magnitude comparison	Compare only magnitude, not sign

Observation	Cause
Sparking while removing woolen sweater over nylon shirt	Static electricity
Repulsion between charged bodies	Sure test of electrification

Fact	Answer
Electrostatics	Study of charges at rest
Positive charge	Deficiency of electrons
Negative charge	Excess of electrons
Charge quantization	\(q=\pm ne\)
Elementary charge	\(1.6\times10^{-19}\ C\)
Charge conservation	Total charge of isolated system remains constant
Like charges	Repel
Unlike charges	Attract
Sure test of electrification	Repulsion
Charge at rest	Produces electric field only
Uniformly moving charge	Produces electric and magnetic fields
Accelerated charge	Emits electromagnetic radiation
Best charging method	Induction
Charge on conductor	Resides on outer surface
Coulomb law valid for	Point charges
Coulomb force depends on	Charge, distance and medium
Coulomb force independent of	Mass of charge
Force in vacuum vs dielectric	Force decreases in dielectric
Conductor dielectric constant	\(\infty\)
Insulator dielectric constant	>1
1 C	\(6.25\times10^{18}\) electrons
Van de Graaff generator	Produces high positive potential
Polar dielectric	Centres of positive and negative charges do not coincide
Non-polar dielectric	Centres of positive and negative charges coincide
Gold leaf electroscope	Detects charge by leaf divergence
Soap bubble charged	Radius increases

Fact	Answer
Electrostatics	Study of charges at rest
Charge transfer	Due to transfer of electrons
Positive charge	Electron deficiency
Negative charge	Electron excess
Quantization	\(q=\pm ne\)
Elementary charge	\(e=1.6\times10^{-19}\ C\)
Conservation of charge	Total charge remains constant
Repulsion	Sure test of electrification
Charge in motion	Charge is invariant
Linear charge density	\(\lambda=\frac{q}{l}\)
Surface charge density	\(\sigma=\frac{q}{A}\)
Volume charge density	\(\rho=\frac{q}{V}\)
Coulomb's law
Coulomb constant	\(9\times10^9\ Nm^2C^{-2}\)
Permittivity of free space	\(8.85\times10^{-12}\ C^2N^{-1}m^{-2}\)
Force in medium
Dielectric constant	\(K=\frac{F_{air}}{F_{medium}}\)
Charge induced
Induced charge in conductor	\(-q_{inducing}\)
Induced charge in air/vacuum	0
Identical conductors after contact	\(\frac{q_1+q_2}{2}\) each
Maximum force after dividing charge Q	Each part \(=\frac{Q}{2}\)
Like charges zero force point	Between charges, nearer lower charge
Unlike charges zero force point	Outside charges, nearer lower charge
Equilateral triangle centre charge	\(-\frac{q}{\sqrt3}\)
Square centre charge	\(-\frac{q}{4}(1+2\sqrt2)\)
Line equilibrium centre charge	\(-\frac{Q}{4}\)
Force strength order	\(F_{nuclear}>F_C>F_G\)
Coulomb vs gravitational	Coulomb may attract/repel; gravity always attracts
Gold leaf electroscope	Detects charge
Faraday ice-pail experiment	Induced charge = inducing charge