Physics · Textbook solutions

Electrostatics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 40 questions

8. Electrostatics — worked examples

19 q

Solved Examples

Worked · 19
  1. Solved Ex.8.1
    A sphere of radius 10 cm carries a charge of 1 μC1\,\mu\text{C}. Calculate the electric field (i) at a distance of 30 cm from the center of the sphere (ii) at the surface of the sphere and (iii) at a distance of 5 cm from the center of the sphere.
  2. Solved Ex.8.2
    The length of a straight thin wire is 2 m. It is uniformly charged with a positive charge of 3 μC3\,\mu\text{C}. Calculate (i) the charge density of the wire (ii) the electric intensity due to the wire at a point 1.5 m away from the center of the wire
  3. Solved Ex.8.3
    The charge per unit area of a large flat sheet of charge is 3 μC/m23\,\mu\text{C/m}^2. Calculate the electric field intensity at a point just near the surface of the sheet, measured from its midpoint.
  4. Solved Ex.8.4
    Potential at a point A in space is given as 4×1054 \times 10^{5} V. (i) Find the work done in bringing a charge of 3 μC3\,\mu\text{C} from infinity to the point A. (ii) Does the answer depend on the path along which the charge is brought?
  5. Solved Ex.8.5
    If 120 μJ120\,\mu\text{J} of work is done in carrying a charge of 6 μC6\,\mu\text{C} from a place where the potential is 10 volt to another place where the potential is VV, find VV
  6. Solved Ex.8.6
    A wire is bent in a circle of radius 10 cm. It is given a charge of 250 μC250\,\mu\text{C} which spreads on it uniformly. What is the electric potential at the centre?
  7. Solved Ex.8.7
    A short electric dipole has dipole moment of 1×10−91 \times 10^{-9} C m. Determine the electric potential due to the dipole at a point distance 0.3 m from the centre of the dipole situated a) on the axial line b) on the equatorial line c) on a line making an angle of 60∘60^\circ with the dipole axis.
  8. Solved Ex.8.8
    Two charges 5×10−85 \times 10^{-8} C and −3×10−8-3 \times 10^{-8} C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
  9. Solved Ex.8.9
    A small particle carrying a negative charge of 1.6×10−191.6 \times 10^{-19} C is suspended in equilibrium between two horizontal metal plates 10 cm apart having a potential difference of 4000 VV across them. Find the mass of the charged particle.
  10. Solved Ex.8.10
    Two charges of magnitude 5 nC and −2-2 nC are placed at points (2 cm, 0, 0) and (20 cm, 0, 0) in a region of space, where there is no other external field. Find the electrostatic potential energy of the system.
  11. Solved Ex.8.11
    Calculate the electrostatic potential energy of the system of charges shown in the figure.
  12. Solved Ex.8.12
    Two charged particles having equal charge of 3×10−53 \times 10^{-5} C each are brought from infinity to a separation of 30 cm. Find the increase in electrostatic potential energy during the process.
  13. Solved Ex.8.13
    a) Determine the electrostatic potential energy of a system consisting of two charges −2 μC-2\,\mu\text{C} and +4 μC+4\,\mu\text{C} (with no external field) placed at (−8(-8 cm, 0, 0) and (+8(+8 cm, 0, 0) respectively. b) Suppose the same system of charges is now placed in an external electric field E=A (1/r2)E = A\,(1/r^2), where A=8×105A = 8 \times 10^{5} cm−2^{-2}, what would be the electrostatic potential energy of the configuration
  14. Solved Ex.8.14
    An electric dipole consists of two opposite charges each of magnitude 1 μC1\,\mu\text{C} separated by 2 cm. The dipole is placed in an external electric field of 10510^{5} N C−1^{-1}. Find: (i) The maximum torque exerted by the field on the dipole (ii) The work the external agent will have to do in turning the dipole through 180∘180^\circ starting from the position θ=0∘\theta = 0^\circ
  15. Solved Ex.8.15
    When 10810^{8} electrons are transferred from one conductor to another, a potential difference of 10 VV appears between the conductors. Find the capacitance of the two conductors.
  16. Solved Ex.8.16
    From the figure given below find the value of the capacitance CC if the equivalent capacitance between A and B is to be 1 μF1\,\mu\text{F}. All other capacitors are in micro farad.
  17. Solved Ex.8.17
    A parallel plate capacitor has an area of 4 cm2^2 and a plate separation of 2 mm (i) Calculate its capacitance (ii) What is its capacitance if the space between the plates is filled completely with a dielectric having dielectric constant of constant 6.7.
  18. Solved Ex.8.18
    In a capacitor of capacitance 20 μF20\,\mu\text{F}, the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, what is the new capacitance?
  19. Solved Ex.8.19
    A parallel plate air capacitor has a capacitance of 3×10−93 \times 10^{-9} Farad. A slab of dielectric constant 3 and thickness 3 cm completely fills the space between the plates. The potential difference between the plates is maintained constant at 400 volt. What is the change in the energy of capacitor if the slab is removed?

Exercises

21 q

Choose the correct option

Practice · 5
  1. Choose the correct option
    Ex Q.1 (i)
    A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential, capacitance respectively are
    1. A.
      Constant, decreases, decreases
    2. B.
      Increases, decreases, decreases
    3. C.
      Constant, decreases, increases
    4. D.
      Constant, increases, decreases
  2. Ex Q.1 (ii)
    A slab of material of dielectric constant kk has the same area A as the plates of a parallel plate capacitor and has thickness (3/4 d)(3/4\,d), where dd is the separation of the plates. The change in capacitance when the slab is inserted between the plates is
    1. A.
      C=Aε0d(k+34k)C = \dfrac{A\varepsilon_0}{d}\left(\dfrac{k+3}{4k}\right)
    2. B.
      C=Aε0d(2kk+3)C = \dfrac{A\varepsilon_0}{d}\left(\dfrac{2k}{k+3}\right)
    3. C.
      C=Aε0d(k+32k)C = \dfrac{A\varepsilon_0}{d}\left(\dfrac{k+3}{2k}\right)
    4. D.
      C=Aε0d(4kk+3)C = \dfrac{A\varepsilon_0}{d}\left(\dfrac{4k}{k+3}\right)
  3. Ex Q.1 (iii)
    Energy stored in a capacitor and dissipated during charging a capacitor bear a ratio.
    1. A.
      1:1
    2. B.
      1:2
    3. C.
      2:1
    4. D.
      1:3
  4. Ex Q.1 (iv)
    Charge +q+q and −q-q are placed at points A and B respectively which are distance 2L apart. C is the mid point of A and B. The work done in moving a charge +Q+Q along the semicircle CRD as shown in the figure below is
    1. A.
      −qQ6πε0L\dfrac{-qQ}{6\pi\varepsilon_0 L}
    2. B.
      qQ2πε0L\dfrac{qQ}{2\pi\varepsilon_0 L}
    3. C.
      qQ6πε0L\dfrac{qQ}{6\pi\varepsilon_0 L}
    4. D.
      −qQ4πε0L\dfrac{-qQ}{4\pi\varepsilon_0 L}
  5. Ex Q.1 (v)
    A parallel plate capacitor has circular plates of radius 8 cm and plate separation 1mm. What will be the charge on the plates if a potential difference of 100 V is applied?
    1. A.
      1.78×10−81.78 \times 10^{-8} C
    2. B.
      1.78×10−51.78 \times 10^{-5} C
    3. C.
      4.3×1044.3 \times 10^{4} C
    4. D.
      2×10−92 \times 10^{-9} C

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (i)
    A charge qq is moved from a point A above a dipole of dipole moment pp to a point B below the dipole in equitorial plane without acceleration. Find the work done in this process.
  2. Ex Q.2 (ii)
    If the difference between the radii of the two spheres of a spherical capacitor is increased, state whether the capacitance will increase or decrease.
  3. Ex Q.2 (iii)
    A metal plate is introduced between the plates of a charged parallel plate capacitor. What is its effect on the capacitance of the capacitor?
  4. Ex Q.2 (iv)
    The safest way to protect yourself from lightening is to be inside a car. Justify.
  5. Ex Q.2 (v)
    A spherical shell of radius b with charge Q is expanded to a radius a. Find the work done by the electrical forces in the process.

Solve the following

Practice · 11
  1. Ex Q.3
    A dipole with its charges, −q-q and +q+q located at the points (0, -b, 0) and (0 +b, 0) is present in a uniform electric field E whose equipotential surfaces are planes parallel to the YZ planes. (a) What is the direction of the electric field E? (b) How much torque would the dipole experience in this field?
  2. Ex Q.4
    Three charges −q-q, +Q+Q and −q-q are placed at equal distance on straight line. If the potential energy of the system of the three charges is zero, then what is the ratio of Q:qQ:q?
  3. Ex Q.5
    A capacitor has some dielectric between its plates and the capacitor is connected to a DC source. The battery is now disconnected and then the dielectric is removed. State whether the capacitance, the energy stored in it, the electric field, charge stored and voltage will increase, decrease or remain constant.
  4. Ex Q.6
    Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors C1C_1 and C2C_2 with their capacitances in the ratio 1:2, so that the energy stored in these two cases becomes the same.
  5. Ex Q.7
    Two charges of magnitudes −4Q-4Q and +2Q+2Q are located at points (2a, 0) and (5a, 0) respectively. What is the electric flux due to these charges through a sphere of radius 4a with its centre at the origin?
  6. Ex Q.8
    A 6 μF6\,\mu\text{F} capacitor is charged by a 300 V supply. It is then disconnected from the supply and is connected to another uncharged 3 μF3\,\mu\text{F} capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation ?
  7. Ex Q.9
    One hundred twenty five small liquid drops, each carrying a charge of 0.5 μC0.5\,\mu\text{C} and each of diameter 0.1 m form a bigger drop. Calculate the potential at the surface of the bigger drop.
  8. Ex Q.10
    The dipole moment of a water molecule is 6.3×10−306.3 \times 10^{-30} Cm. A sample of water contains 102110^{21} molecules, whose dipole moments are all oriented in an electric field of strength 2.5×1052.5 \times 10^{5} N /C. Calculate the work to be done to rotate the dipoles from their initial orientation θ1=0\theta_1 = 0 to one in which all the dipoles are perpendicular to the field, θ2=90∘\theta_2 = 90^\circ.
  9. Ex Q.11
    A charge 6 μC6\,\mu\text{C} is placed at the origin and another charge −5 μC-5\,\mu\text{C} is placed on the y axis at a position A (0, 6.0) m. a) Calculate the total electric potential at the point P whose coordinates are (8.0, 0) m b) Calculate the work done to bring a proton from infinity to the point P. What is the significance of the sign of the work done ?
  10. Ex Q.12
    In a parallel plate capacitor with air between the plates, each plate has an area of 6×10−3 m26 \times 10^{-3}\,\text{m}^2 and the separation between the plates is 2 mm. a) Calculate the capacitance of the capacitor, b) If this capacitor is connected to 100 V supply, what would be the charge on each plate? c) How would charge on the plates be affected if a 2 mm thick mica sheet of k=6k = 6 is inserted between the plates while the voltage supply remains connected ?
  11. Ex Q.13
    Find the equivalent capacitance between P and Q. Given, area of each plate = A and separation between plates = d.