Numericals » 07-Numerical Problems

“Electrostatic” Numerical Problems

Try to solve the following “Electrostatic” numerical problems to clear the concepts in solving the numerical problems.

First of all go to the theory portion of the respective topic and then try to solve the numerical problems by yourself. If facing problem in solving the numerical, click on the Go to solution button to see the ready made solution placed at the bottom of each numerical problem.


01. PROBLEM – P070101

Two identical spheres A and B each having charge ( 6.5 \times 10^{-7} C )  are separated by a distance of ( 50 \ cm ) in air. A third uncharged sphere of same size is brought in contact with the first, then brought in contact with the second and afterwards removed from both. What is the new electrical force between the first two spheres?


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Properties of electrostatic charges.

02. PROBLEM – P070102

An electron falls through a distance of ( 4 \ cm ) in a uniform electric field of value ( 5 \times 10^{4} ) . When the direction of the field is reversed, a proton falls through the same distance. Calculate the (i) acceleration, (ii) time of fall in each case.

Explain why the effect of gravity is not considered in such case.


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Kinematic equations of motion.

03. PROBLEM – P070103

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of   30 \degree with each other. When this set up is suspended in a liquid of density ( 0.8 \ gm \ cm^{-3} ) , the angle remains the same.

DIELECTRIC CONSTANT OF LIQUID
PROBLEM FIGURE P070103

What is the dielectric constant of the liquid? Given – density of the material of the sphere is ( 1.6 \ gm \ cm^{-3} ) .


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Dielectric constant.
  3. Density of matter.

04. PROBLEM – P070104

Two small balls, each of mass m and carrying equal charges are suspended from a point through silk threads of length ( l ) each. The distance between the balls in the steady state is ( x ) where ( x << l ) .

COULOMB'S CONSTANT FOR CHARGED PARTICLE
PROBLEM FIGURE P070104

At what rate the charges from the balls should leak so that the balls may attract each other with a relative velocity, \left [ v = \left ( \frac {a}{\sqrt {x}} \right ) \right ] where ( a ) is a constant. Take coulomb’s constant as ( k ) .


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Dielectric constant.
  3. Resolution of force into rectangular components.

05. PROBLEM – P070105

A charge of ( 4 \times 10^{- 8} C ) is distributed uniformly on the surface of a sphere of radius ( 1 \ cm ) . It is covered by a concentric, hollow conducting sphere of radius ( 5 \ cm ) .

  1. Find the electric field at a point ( 2 \ cm ) away from the centre.
  2. A charge of ( 6 \times 10^{- 8} C )  is placed on the hollow sphere. Find the surface charge density on the outer surface of the hollow sphere.

Keywords related to this problem.

  1. Gauss Law.
  2. Gaussian surface.
  3. Electric field by a charged spherical shell.

06. PROBLEM – P070106

Three concentric thin spherical shells A \ B \ \& \ C of radii ( a ), \ ( b ) \ \& \ ( c ) respectively are placed as shown in figure. The shells A and C are given charges ( q ) and ( - q ) respectively and the shell B is earthed.

DISTRIBUTION OF CHARGE ON THREE CONCENTRIC THIN SPHERICAL SHELLS
PROBLEM FIGURE P070106

Find the charges appearing on the surfaces of B and C .


Keywords related to this problem.

  1. Gauss Law.
  2. Gaussian surface.
  3. Electric field by a charged spherical shell.

07. PROBLEM – P070107

Two conducting plates A and B are placed parallel to each other. A is given a charge ( Q_1 ) and B a charge ( Q_2 ) .

DISTRIBUTION OF CHARGE ON PARALLEL PLATES
PROBLEM FIGURE P070107

Find the distribution of charges on the four surfaces.


Keywords related to this problem.

  1. Surface charge distribution.
  2. Gaussian surface.
  3. Electric field by charged plate.

08. PROBLEM – P070108

A charge ( Q ) is placed at a distance of \left ( \frac {a}{2} \right ) above the centre of a horizontal square surface of edge ( a ) as shown in figure.

GAUSS LAW FOR FLUX THROUGH THE RECTANGULAR PLATE
PROBLEM FIGURE P070108

Find the flux of the electric field through the square surface.


Keywords related to this problem.

  1. Gauss Law.
  2. Gaussian surface.
  3. Application of gauss law.

09. PROBLEM – P070109

A charge ( Q )  is placed at the centre of an imaginary hemispherical surface.

FLUX DISTRIBUTION FOR CHARGE PLACED AT CENTER OF A HEMISPHERE
PROBLEM FIGURE P070109

Using symmetry arguments and the Gauss law, find the flux of the electric field due to this charge through the surface of the hemisphere.


Keywords related to this problem.

  1. Gauss Law.
  2. Gaussian surface.
  3. Electric field by a charged solid sphere.

10. PROBLEM – P070110

A charge of ( 2 \times 10^{- 9} C )  is placed on a corner of a cube of side ( 1 \ m ) as shown in figure.

DISTRIBUTION OF FLUX FOR A CHARGE PLACED AT THE CORNER OF A CUBE
PROBLEM FIGURE P070110

Find the (a) Electric flux passing through this cube (b) Find the flux passing through a face of the given cube.


Keywords related to this problem.

  1. Gauss Law.
  2. Gaussian surface.
  3. Application of gauss law.

11. PROBLEM – P070111

Two identical parallel plate capacitors A and B are connected to a battery of ( V ) volt with the switch S closed as shown in figure. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric medium of dielectric constant ( K ) .

ENERGY STORED IN PARALLEL PLATE CAPACITOR
PROBLEM FIGURE P070111

Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.


Keywords related to this problem.

  1. Capacitor & capacitance.
  2. Effect of dielectric on capacitance.
  3. Effect of dielectric on energy of a capacitor.

12. PROBLEM – P070112

Electric field at a point due to a point charge is ( 20 \ N \ C^{- 1} ) and the electric potential at that point is, ( 10 \ J \ C^{- 1} ) . Calculate the distance of the point from the charge and the magnitude of the charge.


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Electric field by a point charge.
  3. Electric potential at a point in electric field.

13. PROBLEM – P070113

Three charges  ( - q ), \ ( + Q ) \ \& \ ( - q ) are placed at equal distances on a straight line. If the total potential energy of the system is zero, then find the ratio \left ( \frac {Q}{q} \right )  


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Electric field by a point charge.
  3. Electric potential energy.

14. PROBLEM – P070114

A student requires a capacitor of ( 3 \mu F ) in a circuit across a potential of ( 1000 \ V ) . A large number of ( 2 \mu F ) capacitors are available to him each of which can withstand a potential difference of not more than ( 300 \ V ) .

How the student should arrange these capacitors so that he may need minimum number of capacitors?


Keywords related to this problem.

  1. Capacitor & capacitance.
  2. Combination of capacitors.

15. PROBLEM – P070115

Two circular loops of radius ( 0.5 \ m ) and ( 0.09 \ m ) respectively are put such that their axis coincides and their centres are ( 0.12 \ m ) apart as shown in figure. Charge of ( 1 \times 10^{- 6} C )  is spread uniformly on each loop.

POTENTIAL DIFFERENCE BETWEEN TWO CONCENTRIC CIRCULAR LOOPS
PROBLEM FIGURE P070115

Find the potential difference between the centres of loops.


Keywords related to this problem.

  1. Coulomb’s law of electrostatic forces.
  2. Electric field by a charged ring.
  3. Electric potential at a point in electric field.

16. PROBLEM – P070116

Find the equivalent capacitance between the terminals A and B in the given figure. Given, ( C = 1 \mu F )

EQUIVALENT CAPACITANCE OF MIXED COMBINATION OF CAPACITORS
PROBLEM FIGURE P070116

Keywords related to this problem.

  1. Capacitor & capacitance.
  2. Combination of capacitors.

17. PROBLEM – P070117

Calculate the capacitance between the points A and B of the arrangement shown in the figure (A) and (B), if the area of each plate is ( A ) and distance between successive plates is ( d )  .

EQUIVALENT CAPACITANCE
PROBLEM FIGURE P070117

Keywords related to this problem.

  1. Capacitor & capacitance.
  2. Combination of capacitors.

18. PROBLEM – P070118

How many electrons per second flow through the cross section of a conductor so that the conductor carries a current of ( 1 \ A ) ampere?


Keywords related to this problem.

  1. Electric current.

19. PROBLEM – P070119

In an atom, an electron revolves round the nucleus in a circular orbit at the rate of ( 10^5 ) revolutions per second. Calculate the equivalent current. Take ( e = 1.6 \times 10^{-19} \ C )


Keywords related to this problem.

  1. Electric current.

20. PROBLEM – P070120

(a) Estimate the average drift speed of conduction electrons in a copper wire of cross sectional area ( 1.0 \times 10^{-7} \ m^2 ) carrying a current of ( 1.5 \ A ) . Assume that each copper atom contributes one conduction electron. The density of copper is ( 9.0 \times 10^3 \ kg-m^3 ) and its atomic mass is ( 63.5 \ u )

(b) Compare the drift speed obtained above with (i) thermal speed of electrons carrying the current and (ii) speed of propagation of electric field along the conductor which causes the drift motion.

Given, Avogadro’s number is ( N = 6.0 \times 10^{23} ) per kg – atom. Boltzmann constant is ( k = 1.38 \times 10^{-23} \ J K^{-1} ) , mass of electron is ( 9.1 \times 10^{-31} \ kg )


Keywords related to this problem.

  1. Electric current.
  2. Drift velocity.
  3. Boltzmann’s constant.
  4. Avogadro’s number.

21. PROBLEM – P070121

In a discharge tube, the number of hydrogen ions (i.e. protons) drifting across a cross section per second is ( 1.0 \times 10^{18} ) , while the number of electrons drifting in the opposite direction across that cross section is ( 2.7 \times 10^{18} )  per second. If the supply voltage is ( 230 \ V ) , what is the effective resistance of the tube?


Keywords related to this problem.

  1. Electric current.
  2. Drift velocity.
  3. Ohm’s law.

22. PROBLEM – P070122

A resistor of ( 24 \ \Omega ) resistance is bent in the form of a circle as shown in figure. What is the effective resistance between points A and B ?

EFFECTIVE RESISTANCE
PROBLEM FIGURE P070122

Keywords related to this problem.

  1. Ohm’s law.
  2. Parallel combination of resistances.

23. PROBLEM – P070123

A ( 500 \ W ) lamp gives light for 10 hours on electric mains. Find the cost of electric consumption for 30 days if cost of energy is ( Rs. \ 3.00 ) per unit.


Keywords related to this problem.

  1. Ohm’s law.
  2. Electric energy.

24. PROBLEM – P070124

A given wire is stretched to reduce its diameter to half of its original value. What will be its new resistance?


Keywords related to this problem.

  1. Electric resistance.
  2. Factors affecting resistance of a conductor.

25. PROBLEM – P070125

Find the internal resistance of a cell having e.m.f of ( 2 \ V ) . The potential difference across the terminals of this cell drops to ( 1 \ V ) when a resistance of ( 10 \ \Omega ) is connected across it.


Keywords related to this problem.

  1. Electric resistance..
  2. Internal resistance of a cell.

26. PROBLEM – P070126

Calculate the potential difference between B and D points in the given figure. An e.m.f of ( 12 \ V ) is connected in the circuit.

EQUIVALENT RESISTANCE OF MIXED COMBINATION OF RESISTANCE
PROBLEM FIGURE P070126

Keywords related to this problem.

  1. Electric resistance..
  2. Kirchoff’s law.

27. PROBLEM – P070127

A battery of e.m.f ( 10 \ V ) and internal resistance ( 0.5 \ \Omega ) is charged by a d.c. source of ( 12 \ V ) with the help of a series resistor of ( 9.5 \ \Omega ) . Find the terminal voltage of the battery when it is being charged.


Keywords related to this problem.

  1. Electric resistance..
  2. Internal resistance of a cell.
  3. Charging of a cell / battery.

28. PROBLEM – P070128

Two cells of e.m.f of ( 1 \ V  ) and ( 2 \ V ) and internal resistances of ( 2 \ \Omega ) and ( 1 \ \Omega ) respectively, are connected in (i) series (ii) parallel. What should be the external resistance ( R ) in the circuit so that the current through the resistance be the same in the two cases?


Keywords related to this problem.

  1. Ohm’s law.
  2. Combination of resistors.
  3. Combination of cells.

29. PROBLEM – P070129

Find the equivalent resistance between the points a \ \& \ c of the network shown in figure. Each resistance is equal to ( r ) .

EQUIVALENT RESISTANCE OF MIXED COMBINATION OF RESISTORS
PROBLEM FIGURE P070129

Keywords related to this problem.

  1. Ohm’s law.
  2. Combination of resistors.
  3. Kirchoff’s law.

30. PROBLEM – P070130

Twelve wires, each of resistance ( r ) ohms are connected in the form of a skeleton cube. Find the equivalent resistance of the cube when the current enters at one corner and leaves at the diagonally opposite corner.

EQUIVALENT RESISTANCE OF A CUBE OF RESISTOR WIRES
PROBLEM FIGURE P070130

Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.

31. PROBLEM – P070131

Twelve wires, each of resistance ( r ) ohms are connected in the form of a skeleton cube. Find the equivalent resistance between the ends of a face diagonal such as A \ \& \ C .

EQUIVALENT RESISTANCE OF 12 RESISTORS IN A CUBE
PROBLEM FIGURE P070131

Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.

32. PROBLEM – P070132

Twelve wires, each of resistance ( r ) ohms are connected in the form of a skeleton cube. Find the equivalent resistance between the ends of an edge such as A \ \& \ B .

TWELVE RESISTANCES IN FORM OF A SKELETON OF CUBE
PROBLEM FIGURE P070132

Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.

33. PROBLEM – P070133

Find the currents in the different resistors shown in figure.

CURRENT IN A CIRCUIT
PROBLEM FIGURE P070133

Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.

34. PROBLEM – P070134

In the circuit shown in figure E, \ F, \ G \ \& \ H  are cells of e.m.f ( 2 \ V ), \ ( 1 \ V ), \ ( 3 \ V ) \ \& \ ( 1 \ V ) respectively. The resistances ( 2 \ \Omega ), \ ( 1 \ \Omega ), \ ( 3 \ \Omega ) \ \& \ ( 1 \ \Omega ) are their respective internal resistances. Calculate (a) the potential difference between B and D and (b) the potential differences across the terminals of each of the cells G and H .

CURRENT IN A RESISTANCE CIRCUIT
PROBLEM FIGURE P070134

Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.

35. PROBLEM – P070135

A part of a circuit in steady state along with the currents flowing in the branches, the values of resistances etc. is shown in figure.

EQUIVALENT EMF IN A CIRCUIT
PROBLEM FIGURE P070135

Calculate the energy stored in the Capacitor.


Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.

36. PROBLEM – P070136

In the meter bridge experimental set up shown in figure, the null point 'D' is obtained at a distance of ( 40 \ cm ) from end A of the meter bridge wire. If a resistance of ( 10 \ \Omega ) is connected in series with ( R_1 ) , null point is obtained at AD = ( 60 \ cm ) . Calculate the values of ( R_1 ) \ \& \ ( R_2 ) .

FINDING UNKNOWN RESISTANCE WITH METER BRIDGE
PROBLEM FIGURE P070136

Keywords related to this problem.

  1. Metre bridge.
  2. Kirchoff’s law.

37. PROBLEM – P070137

In the given circuit AB is a uniform wire of ( 10 \ \Omega )  and length ( 1 \ m ) . It is connected to series arrangement of cell E_1 of e.m.f ( 2 \ V ) and negligible internal resistance and a resistor ( R ) . Terminal A is also connected to an electro-chemical cell E_2 of e.m.f ( 100 \ mV ) and a galvanometer G . In this set up a balancing point is obtained at ( 40 \ cm ) mark from A . Calculate the resistance ( R ) . If E_2 were to have an e.m.f of ( 300 \ mV ) , where will you expect the balancing point to be?

NULL POINT OF A METER BRIDGE
PROBLEM FIGURE P070137

Keywords related to this problem.

  1. Metre bridge.
  2. Kirchoff’s law.

38. PROBLEM – P070138

Find the equivalent resistance between the points ( a ) \ \& \ ( b )  of the infinite ladder shown in figure.

EQUIVALENT RESISTANCE OF A LADDER OF INFINITE IDENTICAL RESISTANCES
PROBLEM FIGURE P070138

Keywords related to this problem.

  1. Combination of resistors.
  2. Kirchoff’s law.