CBSE Class 12 Physics HOTs Electrostatic Potential and Capacitance

  UNIT 01

ELECTROSTATICS

ONE MARK QUESTIONS

Question. Define the term ‘potential energy’ of charge ‘q ‘at a distance ‘r’ in an external electric field.
Answer : It is defined as the amount of work done in bringing the charge q from infinity to the location ‘r’ in an external electric field.

Question. Name the physical quantity whose SI unit is J/C. is it scalar or vector quantity?
Answer : Electrostatic potential. Scalar quantity

Question. A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. what is potential at the centre of the sphere?
Answer : 10 V

Question. A charge ‘q’ is placed at the centre of a cube of side l, what is the electric passing through each face of the cube?
Answer : Flux linked through each face of the cube =q/6ɛ0

Question. Two equal balls having equal positive charge ’q’ coulombs are suspended by two strings of equal length. What would be the effect on the force when a plastic sheet is inserted between the two?
Answer : The will be reduced as force is inversely proportional to the dielectric constant K. for plastic K˃ 1.

Question. A point charge +Q is placed in the vicinity of a conducting surface. Trace the field lines between the charge and the conducting surface.
Answer : 

Question. Name the physical quantities whose S.I. units are (i) coulomb/volt (ii) N/C (iii) V/m.
Answer : (i) Capacitance (ii) Electric field intensity (iii) Electric field intensity. 

Question. What is the electric flux passing through two opposite faces of the cube?
Answer : Flux linked through two opposite faces of the cube=q/3 ɛ0

Question. Two charges of magnitude -2Q and +Q are located at points (a,o) and (4a, o) respectively. What is the electric flux due these charges through a sphere of radius ‘3a’ with its centre at the origin?
Answer : Flux= -2Q/ ɛ0

Question. Two charges of magnitude -3Q and +2Q are located at points (a,o) and (4a, o) respectively. What is the electric flux due these charges through a sphere of radius ‘5a’ with its centre at the origin?
Answer : Flux= Q/ ɛ0

THREE MARKS QUESTIONS

Question. A sphereS1 of radius r1 encloses a net charge Q. If there is another concentric sphere S2 of radius r2 (r2˃ r1) enclosing charge 2Q.
Answer :
(i) Find the ratio of the electric flux through sphere S1 and S2.
(ii) How will the electric flux through sphere S1 change, if a medium of dielectric constant 5 is introduced in the space inside S1 in place of air?
Answer : (i) Ф1 = Q/εo, Ф2= 3Q/εo Ф1/Ф2 =1/3
ii) if a dielectric medium of dielectric constant 5 is inserted then
Ф1’ =Q/5εo= Ф1/5

Question. Two capacitors of unknown capacitances C1 and C2 are connected first in series and then in parallel across a 100 V battery. If the energy stored in the two combinations is 0.045J and 0.25 J respectively, then determine the value of C1 andC2. Also calculate the charge on each capacitor in parallel combination.
Answer : Energy stored in series combination is
Es = 1/2CsV2 =C1C2x(100)2/2(C1+C2) =0.045J ----------(1)
Energy stored in parallel combination is
Ep= ½ CpV2 =1/2 (C1+C2)V2 = 0.25 J-----------------------(2)
On solving equations 1 and 2 we get
C1= 35µF and C2 =15µF
Q1 = 35x10-4C and Q2 =15x10-4C

Question. Four point charges Q, q, Q and q are placed at the corners of a square of side ‘a’ as shown in the figure.
Find the
a) Resultant electric force on a charge Q, and
b) Potential energy of this system.
Answer : The resultant force on the charge Q is given by
FQ = 1/4πɛoa(2Qq)1/2
Potential energy of the system = 1/4πɛ₀[qQ/a+QQ/a√2+qQ/a+qQ/a√2+qQ/a+qQ/a]
= 1/4πɛ₀[3qQ/a+(Q2+qQ/a√2)]

Question. a. Three point charges q, -4q and 2q are placed at the vertices of an equilateral triangle ABC of side ‘ l’ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q.
Find out the amount of work done to separate the charges at infinite distance.
Answer : a. The magnitude of the resultant electric force acting on the charge q is given by
Fq=1/4πɛ₀[(-4q)(q)/l2+(2q)(q)/l2]
= -2q2/4πɛ₀l2
b. The work done to separate the charges at infinite distance = -potential energy of the system
=1/4πɛ₀[(-4q)(q)/l+(2q)(q)/l+(-4q)(2q)/l]
= +[10q2/4πɛ₀]

Question. Calculate the equivalent capacitance between points A and B in the circuit below. If a battery of 10 V is connected across A and B, calculate the charge drawn from the battery by the circuit.
Answer : Since C1 /C2 = C3/C4
This is the condition of balance so there will be no current across PR
Now C1 and C2 are in series,
So C12 = 20/3 µF
again C3 and C4 are in series
So, C34 = 10/3µF
Equivalent capacitance between A and B is CAB = C12+ C34 = 10 µF.
Charge drawn from battery Q = CV = 10x10µC = 100µC

FIVE MARKS QUESTIONS

Question. Derive an expression for the energy stored in a parallel plate capacitor.
On charging a parallel plate capacitor to a potential V, the spacing between the plates is halved, and a dielectric medium of ɛr =10 is introduced between the plates, without disconnecting the d.c. source. Explain using suitable expression, how the (i) capacitance, (ii) electric field and (iii) energy stored in the capacitor change.
Answer : For energy stored, see the NCERT Text Book.
When capacitor is charged by a battery and remains connected, the potential difference remains same, equal to V.
(i) C =ɛoA/d d’ = d/2 and ɛ r = 10
So, C’ = ɛrɛoA/d/2 = 2ɛr ɛoA/d = 2x10C = 20C
(ii) E =V/d E’ = V/d/2 = 2 V/d = 2 E
(iii) Energy density initially, U = ½ ɛoE2
Energy density finally , U’= ½ ɛrɛoE’2 = 40 U

Question. a. Deduce the expression for the torque acting on a dipole of dipole moment P in the presence of a uniform electric field.
b. Consider two hollow concentric spheres, S1 and S2, enclosing charges 2Q and 4Q respectively as shown in figure.
(i) find out the ratio of electric flux through them.
(ii) How will the electric flux through the space S1 change if a medium of dielectric constant ɛr is introduced in the space inside S1 in place of air? Deduce the necessary expression.
Answer : Consider an electric dipole of charge –q and +q and of length 2a placed in a uniform electric field E making an angle ɵ with electric field.
Force on charge –q = -qE force on charge +q = +qE electric dipole is under the action of two equal and opposite unlike parallel forces, which give rise to a torque on the dipole.
Ϯ = qE(AN)
= q(2a)Esinɵ = PEsinɵ
Ϯ = PXE
b. (i) Charge enclosed by sphereS1 = 2Q
Electric flux through the sphereS1 is, Ф= 2Q/ɛ₀
Charge enclosed by sphereS2 =2Q+4Q = 6Q
Electric flux through the sphereS21 is, Ф1= 6Q/ɛ₀
Ratio is given by Ф/Ф1 = 1:3
(ii) for sphere S1, the electric flux is Ф’ = 2Q/ɛr
Ф’/Ф1= 2Q/ɛr/6Q/ɛ₀ = ɛr/ɛ₀.1/3
Since ɛr>ɛ₀ , Ф’< Ф1
Therefore the electric flux through the sphere S1 decreases with the introduction of the dielectric medium.

Question.a) Define electric flux. Is it a scalar or a vector quantity?
A point charge ‘q’ is at a distance of d/2 directly above the centre of a square of side d, as shown in the figure. Use Gauss’ Law to obtain the expression for the electric flux through the square.
b) If the point charge is now moved to a distance ‘d’ from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected?
Answer : a) The number of electric field lines passing through an area normally is called electric flux.
It is a scalar quantity.
Here the given square of side d is one face of the cube of side a. At the centre of the cube a charge q is placed.
According to Gauss’ theorem the total electric flux through the six faces of the cube = q/εo
So the total electric flux through the square = q/6ε0
b.If the point charge is moved to a distance ‘d’ from the centre of the square and the side of the square is doubled then there will be no change in the electric flux . As here also the charge is at the centreof the cube.

Question. (a) Define electric flux. Write its SI unit.
(b) The electric field components due to a charge inside the cube of side 0.1 m . Ex = αx where α = 500 N/Cm
Ey = 0, Ez = 0
Calculate (i) the flux through the cube, and (ii) the charge inside the cube.
Answer : The number of electric field lines passing through an area normally is called electric flux.
Its SI unit is Nm2C-1 or JmC-1 or Vm.

Q.1 A certain region has cylindrical symmetry of electric field. Name the charge distribution producing such a field.

Q.2 Represent graphically the variation of electric field with distance, for a uniformly charged plane sheet.

Q.3 How will the radius of a flexible ring change if it is given positive charge? 

Q.4 Five Charges of equal amount (q) are placed at five corners of a regular hexagon of side 10 cm. What will be the value of sixth charge placed at sixth corner of the hexagon so that the electric field at the center of hexagon is zero? 

Q.5 Two conducting spheres of radii r1 & r2 are at same potential. What is the ratio of charges on  he spheres?.

Q.6 Why do we use nitrogen or methane gas in Van-de-Graff generator?

Q.12 A charged particle is free to move in an electric field. Will it always move along an electric line of force? Justify your answers?.

 

(2 marks)

Q.13 The flux of the electrostatic fields, through the closed spherical surface S,’ is found to be four times that through the closed sphere ‘S1’. Find the magnitude of the charge Q . Given, q1= 1 μc,q2=-2μc and q3=9.854 μc (2 marks)

Q.14 A charge Q is divided in two parts q and Q - q separated by a distance R. If force between the two charges is maximum, find the relationship between q & Q. (2 marks)

 

Q.15 A capacitor is made of a flat plate of area A and second plate having a stair like structure as shown in figure below. If width of each stair is A/3 and height is d. Find the capacitance of the arrangement.

(2 marks)

Q.2 E is constant with r.

Q3. Increases due to repulsion

Q.4 6th Charge is Q

Q.5 Q₁/Q₂=R₁/R₂

Q.6 It transfers the leakage of Charge to earth through earthed steel chamber

Q.7 Q/24 έ₀

Q.8 Zero

Q9. Ex=Ez<Ey

Q.10 E α 1/r³ if r=r/2 , E= 8 times

 

2 marks question

Q 11 work done is independent of path w= ¼πεΟ q₁ q₂ ( 1/r₁- 1/r₂) putting the values & ans 15 J

 

Q 12 if charge is positive & at rest in electric field then it will move along electric line of force. If charge has initial velocity making some angle with electric field than it will along parabolic path.

 

Q 13 Ф'= 4Ф

Q + q₁+ q₂+q₃/ εo= 4 X (q₁+q₂+q₃)/εo putting the values & finding Q = 3*8.854 μC

 

Q 14. F=K q(Q-q) / r 2 for max. &min.dF / dq=0 , q=Q/2

 

Q 15. All are in parallel

C= ε_oA/3d+ε_oA/6d+ ε_oA/9d= 11ε_oA/18 d

 

3 marks question

Q.16 a. E same

b. Q same

c. V same

d. C is halved with reasons

 

Q.17 i. N times the charge on small drop

ii. N 2/3 times the potential on small drop

iii N 1/3 times the capacitance on small drop

 

Q.18 If q is moved along abcd then Wabcda = 0

W_ab+ W_bc+ W_cd +W_da = 0

as E perpendicular to bc & da

so W_bc = W_da = 0

therefore W_ab= -W_cd

But W_ab can never be equal to Wcd as the lines of force are closer to cd

therefore W_cd > W_ab

therefore W_abcda is not equal to 0 hence such electric field E is impossible

 

Q.19 i As the charge move closer the charge on large sphere is redistributed as shown in diagram

ii As the spheres move more closer than the charge is redistributed as shown in diagram

iii Behaviour of force between 2 cm & 1 cm : force of repulsion increases upto 1.4 cm & F rep. is max. at r=1.4 cm

UNIT-1

ELECTROSTATICS

1. Where the energy of capacitor does resides?

2. Do electrons tend to go to region of low or high potential?

3. What is the net charge on the charged capacitor?

4. A Gaussian surface encloses an electric dipole within it. What is the total flux across sphere?

5. Find the dimension of 1/2ε_oE².

6. In a certain l m3 of space, electric potential is found to be V Volt throughout. What is the electric field in this Region?

7. If Coulomb law involves 1/r³ instead of 1/r² dependence, would Gauss law be still true?

8. An electrostatic field line can’t be discontinuous, why?