CBSE Class 12 Physics Electrostatistics Assignment

ELECTRIC POTENTIAL & CAPACITORS

Question. A capacitor of capacitance C has a charge Q and stored energy W. If the charge is increased to 2Q, the stored energy will be
(a) 𝑊/4
(b) 𝑊/2
(c) 2W
(d) 4W
Answer. D

Question. A battery is used to charge a capacitor till the potential difference between the plates become equal to the emf (V) of the battery. The ratio of the energy stored in the capacitor to the work done by the battery will be
(a) ½
(b) 2
(c) ¼
(d) 4
Answer. A

Question. The electric potential V at any point (x,y,z) in space is given by V=3x² where x,y,z are all in metre. The electric field at the point (1m,0,2m) is
(a) 6V/m along -x axis
(b) 6V/m along +x axis
(c) 1.5V/m along -x axis
(d) 1.5V/m along +x axis
Answer. A

Question. A parallel plate capacitor with oil in between the plates (dielectric constant of oil is 2) has a capacitance ‘C’. If the oil is removed, what will be the new capacitance
(a) 𝐶√2
(b) 𝐶2
(c) 2𝐶
(d) √2𝐶
Answer. B

Question. A conducting sphere of radius R carrying charge Q lies inside an uncharged conducting shell of radius 2R. If they are connected by a metal wire, the amount of heat that will be produced is
(a) 1/4𝜋𝜀_𝑜. 𝑄²/𝑅
(b) 1/4𝜋𝜀_𝑜. 𝑄²/2𝑅
(c) 1/4𝜋𝜀_𝑜. 𝑄²/3𝑅
(d) 1/4𝜋𝜀_𝑜. 𝑄²/4𝑅
Answer. D

Question. A metallic sphere has a charge of 10μC. A unit negative charge is brought from point A to another point B both 100cm away from the sphere, but A being east of it while B being on west. The net work done is
(a) 2/10J
(b) −1/10𝐽
(c) Zero
(d) Data insufficient
Answer. C

Question. A parallel plate air capacitor having a capacitance ‘C’ is half-filled by a medium of dielectric constant 5. What % change will be there in the capacitance of the capacitor?
(a) 200% increase
(b) 400% decrease
(c) 400% increase
(d) 66.6% increase
Answer. D

Question. Two parallel plate capacitors X and Y have same plate area and same separation between the plates. X has air between the plates and Y has a dielectric medium of K=4. When they are connected in series with a source of 12V, what is the ratio of energies stored in X to Y
(a) 1:4
(b) 8:1
(c) 4:1
(d) √2 :
Answer. C

Question. An electric charge 10^-3 μC is placed at the origin (0,0) of (x, y) co-ordinate system. Two points A and B are situated at (√2,√2) and (2,0) respectively. The potential difference between the points A and B will be
(a) 4.5 V
(b) Zero
(c) 2.0V
(d) 9.0V
Answer. B

Question. Two identical metal plates are given positive charges q₁ and q₂ (q₁> q₂). If they are now brought near to each other to form a capacitor with capacitance C, what will be the potential difference between the plates?
(a) (q₁+q₂)/2C
(b) (q₁+q₂)/C
(c) (q₁- q₂)/C
(d) (q₁-q₂)/2C
Answer. D

Question. Is the electro static potential necessarily be zero at a point where electric field is zero? Justify
Answer. No. 𝐸=−𝑑𝑉/𝑑𝑟. That is, even when E = 0, potential can be a non zero constant

Question. A large hollow metallic sphere A is charged positively to a potential of 100V and a small sphere B to a potential of 50V. Now B is placed inside A and they are connected by a wire. In which direction will the charge flow?
Answer. From B to A. When sphere B is placed inside the sphere A, total potential of B become 150V. So charge flow from higher potential to lower potential. 

Question. How does the energy stored in a capacitor change if after disconnecting from the battery, the plates are moved farther? Justify
Answer. Energy increases. The capacitance, C decreases as plate distance increase. As the battery is disconnected, 𝑈=𝑞²/2𝐶 which will increase

 Assertions & Reasons Questions

Select the most appropriate answer from the options given below:
A) Both A and R are true and R is the correct explanation of A
B) Both A and R are true but R is not the correct explanation of A.
C) A is true but R is false.
D) A is false and R is also false.

Question. A- The work done by an electrostatic field in moving a charge from one point to another depends only on the initial and the final points.
R- Electrostatic force is a conservative fore.
Answer. A

Question. A- For a point charge potential V=kQ/r is applicable for Q>0 &Q<0
R- for Q < 0, the force on a unit positive test charge is attractive
Answer. A

Question. A- The electric field at every point is normal to the equipotential surface passing through that point.
R- No work is required to move a test charge on an equipotential surface.
Answer. A

Question. A- For a uniform electric field E along the x -axis, the equipotential surfaces are planes parallel to the y-z plane.
R- Electric field is in the direction in which the potential increases.
Answer. C

Question. A- A non polar molecule is one in which the centres of positive and negative charges are separated.
R- Non polar molecules have a permanent dipole moment.
Answer. D

Question. A- In an external electric field, the positive and negative charges of a non polar molecule are displaced in opposite directions.
R- Oxygen & Hydrogen are non polar molecules.
Answer. B

Question. A- When a dielectric is inserted between the plates of a capacitor, capacitance increases.
R- The dielectric is polarised by the field.
Answer. A

Question. A- A capacitor with large capacitance can hold large amount of charge Q at a relatively small V.
R- The charge of the capacitor leaks away due to the reduction in insulating power of the intervening medium.
Answer. B

Question. A- When capacitors are connected in series net capacitance decreases.
R- In series combination, charges on the two plates are the same on each capacitor.
Answer. B

Question. A- Two concentric spherical shell of different radius are at potential VA and VB. If outer shell is earthed then potential difference will not be changed.
R- Potential difference between the surfaces of two concentric spherical shells does not depends on the charge on the outer shell.
Answer. D

Question. A- When a capacitor is charged by a battery, both the plates receive charge equal in magnitude, no matter sizes of plates are identical or not.
R -. The charge distribution on the plates of capacitor is in accordance with charge conservation principle
Answer. C

Question. A- When a charged capacitor is filled completely with a metallic slab, its capacitance is increased by a large amount.
R -The dielectric constant for metal is infinite.
Answer. A

Question. A: Electric potential of a positively charged body may be negative.
R - The potential of a conductor does not depend on the charge of the conductor.
Answer. C

Question. A – In the absence of an external electric field, the dipole moment per unit volume of a polar dielectric is zero.
R – The dipoles of a polar dielectric are randomly oriented.
Answer. 

ONE MARK QUESTIONS

Q1 Define electric dipole moment. Write its SI unit.

Q2. A hollow metal sphere of radius 5cm is charged such that the potential on its surface is 10V.What is the potential at the centre of the sphere ?

Q3 Charges of magnitudes 2Q and –Q are located at points (a,0,0) and (4a ,0,0) .Find the ratio of the flux of electric field ,due to these charges ,through concentric spheres of radii 2a and 8a centred at origin ?

Q4 Two electrically charged particles ,having charges of different magnitude ,when placed at a distance d from each other ,experience a force of attraction F .These two particles are put in contact and again placed at the same distance `from each other.What is the nature of new force between them ?Is the magnitude of the force of attraction between them now more or less than F ?

Q5 If the radius of the Gaussian surface enclosing a surface is halved ,how does the electric flux through the Gaussian surface change?

Q6.Draw an equipotential surface for a uniform electric field.

Q7 Name the physical quantity whose SI unit is

(i) Coulomb/volt

(ii) Newton/coulomb.

(iii) Joule/coulomb

Q8 Two electric field lines never cross each other .Why ?

Q9.Is it possible for a metal sphere of 1cm radius to hold a charge of 1C ?

Q10 A charge of 2C moves between two plates maintained at a potential difference of 1 volt .What is the energy acquired by the charge ?

TWO MARKS QUESTIONS

Q11. A thin straight infinitely long conducting wire having charge density λ is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire.Find the expression for the electric flux through the surface of the cylinder.

Q12 Find the amount of work done in rotating an electric dipole of dipole moment 3 x 10-8 Cm from its position of stable equilibrium ,to position of unstable equilibrium , in a uniform electric field of intensity 104 N/C

Q13 Justify that the electrostatic potential is constant through the volume of a charged conductor and has the same value on its surface as inside it.

Q14 A capacitor is charged with a battery and then its plate separation is increased without disconnecting the battery. What will be the change in
(a) Charge stored in the capacitor.
(b) Energy stored in the capacitor
(c) Potential difference across the plates of the capacitor?
(d) Electric field between the plates of the capacitor?

Q16 Using Gauss law establish that the magnitude of electric field intensity , at a point , due to an infinite plane sheet , with uniform charge density σ is independent of the distance of the field point.

Q17. Define an electric field line . Draw the pattern of the field lines around a system of two equal positive charges separated by a distance .

THREE MARKS QUESTIONS

Q18 Two uniformly large parallel thin plates having charge densities +σ and –σ are kept in the X-Z plane at a distance ‘d’ apart.Sketch an equipotential surface due to electric field between the plates.If a particle of mass m and charge –q remains stationary between the plates,what is the magnitude and direction of this field?

Q 19 Using gauss’s law obtain the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point outside the shell.Draw a graph showing the variation of electric field with r,for r> R and r< R.

Q20 Show mathematically that sharing of charges between two capacitors (or conductors) ,is always accompanied with some loss of electrostatic energy.