PHYSICS ASSIGNMENT
CLASS – XII
Chapter – 1 : Electric Charges and Fields
Theory Based Questions:
Q1.(a) State Coulomb’s law of force between charges at rest. Express the same in SI units.
(b)Name and define the SI unit of charge.
(c)Write Coulomb’s law in vector form. What is the importance of expressing it in vector form?
Q2.Define dielectric constant of a medium in terms of force between electric charges, electric field & electrical permittivity.
Q3.Define electric field intensity and derive an expression for it at a point on the axial line of a dipole. Also determine its direction.
Q4.Define electric dipole moment. Derive an expression for the electric field intensity at any point along the equatorial line of an electric dipole.
Q5.(a) Derive an expression for the torque acting on an electric dipole, which is held in uniform electric field, when the axis of the dipole makes an angle with the electric field. Hence define electric dipole moment.
(b)What happens when an electric dipole is held in a non-uniform electric field? What will be the force and the torque when the dipole is held parallel or antiparallel to the electric field?
Q6.Sketch the lines of force of
(i)a point charge q > 0,
(ii)a point charge q < 0,
(iii)an electric dipole or two equal and opposite charges separated by a small distance,
(iv)two equal positive charges placed small distance apart in air, and
(v)a positively charged plane conductor.
Q7.State Gauss’s theorem in electrostatics. Using this theorem, derive an expression for the electric field intensity due to an infinitely long, straight wire of linear charge density .
Q8.(a) Define electric flux.
(b)A point charge is placed at the centre of spherical Gaussian surface. How will electric flux change if
(i)the sphere is replaced by a cube of same or different volume,
(ii)a second charge is placed near, and outside, the original sphere,
(iii)a second charge is placed inside the sphere, and
(iv)the original charge is replaced by an electric dipole?
Q9.Using Gauss Theorem derive an expression for the electric field intensity at a point near a thin infinite plane sheet of charge density .
Q10.Apply Gauss theorem to calculate the electric field due to a uniformly charged spherical shell at a point
(a) outside the shell,(b) on the shell and (c) inside the shell.
Draw a graph showing the variation of electric field E with distance r from the centre of a uniformly charged thin spherical shell.
Numerical Questions :
Q1.Which is bigger – a coulomb or a charge on an electron? How many electronic charges form one coulomb of charge?
Q2.A charge q is placed at the centre of the line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = – Q/4.
Q3.Two similar balls each having mass m and charge q are hung from a silk thread of length l, prove that equilibrium separation
when each thread makes a small angle with the vertical.
Q4.Two small spheres each having mass m kg and charge q coulomb are suspended from a point by insulating threads each I metre long but of negligible mass. If is the angle, each thread makes with the vertical when equilibrium has been attained, show that
Q5.Two point charges q1= + 0.2C and q2 = + 0.4 C are placed 0.1 m apart. Calculate the electric field at (a) the midpoint between the charges. (b) a point on the line joining q1 and q2 such that it is 0.05 m away from q2 and 0.15 m away from q1.
Q6.ABCD is a square of side 5m. Charges of +50 C, – 50 C and + 50 C are placed at A, C and D respectively. Find the resultant electric field at B.
Q7.Electric field in is directed along + X direction and given by , where E is in and is in metre, A and B are constants with dimensions. Talking A = 10 and B = 5 , calculate
(i)the electric flux through the cube.
(ii)net charge enclosed within the cube.
Q8.Two small identical electrical dipoles AB and CD, each of dipole moment ‘p’ are kept at an angle of 120o as shown in Fig. What is the resultant dipole moment of this combination? If this system is subjected to electric fielddirected along + X direction, what will be the magnitude and direction of the torque acting on this?
Q9.(a)Two point charges placed at a distance r in air exert a force F on each other. At what distance will these charges experience the same force F in a medium of dielectric constant K?
(b)A force F is acting between two charges placed some distance apart in vacuum. If a brass rod is placed between these two charges, how does the force change?
Q10.(a)An infinite line charge produces a field of 9 at a distance of 2 cm. Calculate the linear charge density.
(b)Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude . What is E (a) to the left of the plates, (b) to the right of the plates, and (c) between the plates?
(c)A spherical rubber balloon carries a charge that is uniformly distributed over its surface. As the balloon is blown up; how does E vary for points (i) inside the balloon, (ii) on the surface of the balloon and (iii) outside the balloon?
PHYSICS ASSIGNMENT
CLASS – XII
Chapter – 2:Electrostatic Potential & capacitance
Theory Based Questions:
Q1.(a) Define electric potential. Derive an expression for the electric potential at a distance r from a point charge q.
(b) Draw graphs showing the variations of (i) electrostatic potential V and (ii) electrostatic field E with distance r from a charge q.
Q2.Derive an expression for the electric potential due to an electric dipole at any general point.
Q3.(a) What is an equipotential surface? Give an example.
(b) Show that the amount of work done in moving a test charge over an equipotential surface is zero.
(c)Sketch equipotential surface for
(i)a positive point charge
(ii)two equal and opposite charges separated by a small distance.
(iii)two equal and positive charges separated by a small distance.
(iv)a uniform electric field.
Q4.Derive an expression for the potential energy of a dipole in a uniform electric field. Hence discuss the conditions of its stable and unstable equilibrium.
Q5.(a) Derive an expression for the capacitance of a parallel plate capacitor.
(b) What are the factors on which the capacitance of a parallel plate capacitor depends?
Q6.Derive an expression for the energy stored in a parallel plate capacitor. Hence show that electric field E is a source of energy with energy density .
Q7.Two capacitors with capacity and are charged to potentials and respectively and then connected in parallel. Calculate the common potential across the combination, the charge on each capacitor, the electrostatic energy stored in the system and the change in the electrostatic energy from its initial value.
Q8.(a) How does a dielectric develop a net dipole moment in an external electric field when it has (i) non-polar molecules and (ii) polar molecules?
(b) Explain why the polarization of a dielectric reduces the electric field inside the dielectric. Hence define dielectric constant.
Q9.(a) Define polarisation density. How is it related to the induced surface charge density?
(b) Define electric susceptibility. Deduce the relation between dielectric constant and electric susceptibility.
Q10.What is a dielectric? A dielectric slab of thickness t is kept between the plates of a parallel plate capacitor separated by distance d. Derive the expression for the capacitance of the capacitor for t <d.
Numerical Questions:
Q1.Twenty seven drops of same size are charged at 220 V each. They coalesce to form a bigger drop. Calculate the potential of the bigger drop.
Q2.Calculate the electric potential at the centre of a square of side having charges 100 and at the four corners of the square.
Q3.An infinite plane sheet of charge density is held in air. In this situation how far apart are two equipotential surfaces, whose p.d. is 5V?
Q4.An electric dipole of length 4cm, when placed with its axis making an angle of 60o with a uniform electric field experiences a torque of 4 Nm. Calculate the (i) magnitude of the electric field, (ii) potential energy of the dipole, if the dipole has charges of 8 nC.
Q5.An electric dipole consists of two opposite charges each of magnitude 1separated by 2 cm. The dipole is placed in an external electric field of . Find (i) the maximum torque exerted by the field on the dipole (ii) the work which the external agent will have to do in turning the dipole through 180o starting from the position .
Q6.A parallel plate capacitor of 300 is charged to 200 V. If the distance between its plates is halved, what will be the potential difference between the plates and what will be the change in stored energy?
Q7.Two parallel plate capacitors, X and Y, have the same area of plates and same separation between them. X has air between the plates while Y contains a dielectric medium of
(i)Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4
(ii)Calculate the potential difference between the plates of X and Y.
(iii)What is the ratio of electrostatic energy stored in X and Y?
Q8.Keeping the voltage of the charging source constant, what would be the percentage change in the energy stored in a parallel plate capacitor if the separation between its plates were to be decreased by 10%?
Q9.(a) Calculate the capacitance of the capacitor shown in the figure.
(b) Find the capacitance of the infinite network between points A andB.
Q10.Calculate equivalent capacitance between A & B. Also, calculate charge and voltage across each capacitor.
(i) (ii)
(iii)
C1 = C2 = C4 = 5pF C3 = C5 = 10 pF
PHYSICS ASSIGNMENT
CLASS – XII
Chapter – 3 :Current Electricity
Theory Based Questions:
Q1.Give some important points of differences between electromotive force and potential difference.
Q2.Define the terms drift velocity and relaxation time. Derive an expression for the drift velocity of free electrons in a conductor in terms of relaxation time.
Q3.(a) Derive ohm’s law on the basis of the theory of electron drift.
(b) Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time.
Q4.Define internal resistance of a cell. Prove that , where R = external resistance.
Q5.Derive the condition for obtaining maximum current through an external resistance connected across a series combination of cells.
Q6.Derive the condition for obtaining maximum current through an external resistance connected across a parallel combination of cells.
Q7.Derive the condition for obtaining maximum current through an external resistance connected across a mixed grouping of cells.
Q8.State Wheatstone bridge principle. Deduce the condition for which Wheatstone bridge is balanced.
Q9.Define potential gradient. With the help of a circuit diagram, explain how a potentiometer can be used to compare the emfs of two primary cells.
Q10.State the principle of a potentiometer. With the help of a circuit diagram, describe a method to find the internal resistance of a primary cell.
Numerical Questions:
Q1.A current of 2mA is passed through a colour coded carbon resistor with first, second & third rings of yellow, green and orange colours. What is the voltage drop across the resistor?
Q2.(a) A wire has a resistance of . It is melted and drawn into a wire of half its length. Calculate the resistance of the new wire. What is the percentage change in its resistance?
(b) The resistance of a wire is R ohms. What will be its new resistance if it is stretched to ‘n’ times its original length?
Q3.Two wires X, Y have the same resistivity, but their cross – sectional areas are in the ratio 2 : 3 and lengths in the ratio 1 : 2. They are first connected in series and then in parallel to a d.c. source. Find out the ratio of the drift speeds of the electrons in the two wires for the two cases.
Q4.(a) A set of identical resistors, each of resistance , when connected in series have an effective resistance R & when connected in parallel, their effective resistance is Y. Find relation between R, X and Y.
(b) A wire of uniform cross section and length has a resistance of . It is cut into four equal parts. Each part is stretched uniformly to length and all the four stretched parts are connected in parallel. Calculate the total resistance of the combination so formed. Assume that stretching of wire does not cause any change in the density of its material.
Q5.(a) Calculate the current shown by the ammeter A in the circuit shown in figure.
(b) A battery of emf 10V is connected to resistance as shown in figure. Find the potential difference between points A and B,R1 = R4= , R2 = R3 = .
Q6.Calculate equivalent resistance between A & B.
(i) (ii)
Q7.(a) The reading on a high resistance voltmeter when a cell is connected across it is 2.2V. When the terminals of the cell are also connected to a resistance of , the voltmeter reading drops to 1.8V. Find the internal resistance of the cell.
(b)A battery of emj ‘E’ & internal resistance ‘r’ gives a current of 0.5A with an external resistor of 12 & a current of 0.25 A with an external resistor of 25. Calculate internal resistance of the cell & emf of the cell.
Q8.Three cells of emf 2V, 1.8V, 1.5V are connected in series. Their internal resistances are 0.05, 0.7 & 1 respectively. If the battery is connected to an external resistance of 4 via a very low resistance ammeter, what would be the reading in the ammeter?
Q9.Two identical cells of emf 1.5V each joined in parallel provide supply to an external circuit consisting of two resistances of 17 each joined in parallel. A very high resistance voltmeter reads the terminal voltage of cells to be 1.4V. Calculate the internal resistance of each cell.
Q10.12 cells, each of emf 1.5V & internal resistance 0.5 are arranged in m rows each containing n cells connected in series. Calculate the values of n and m for which this combination would send maximum current through an external resistance of 1.5.
Q11.(a) Using kirchoff’s laws, calculate the potential difference across the 8 resistor shown in the figure.
(b)Determine the current in each branch of the network shown in the figure.
(c) In the circuit shown in figure, E, F, G & H are cells of emf 2V, IV, 3V and IV & their internal resistances are 2, 1, 3 1 respectively. Calculate
(i) potential difference between B and D.
(ii)potential difference across the terminals of each of the cells G and H.
Q12.(a)A galvanometer of 15resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.
(b)Calculate equivalent resistance across points A and B.
Q13.(a)In the following circuit, a metre bridge is shown in its balanced state. The meter bridge wire has a resistance of 1 ohm/cm. Calculate the value of ‘X’ and the current drawn from the battery of negligible internal resistance.
(b)In a metre bridge, the null point is found at ‘l1’, from A. If now a resistance ‘X’ is connected in parallel with ‘S’, the null point occurs at ‘l2’from A. Obtain formula for X in terms of and S.
Q14.(a)Two cells of emfs, E1 & E2 (E1 < E2) are connected as shown in figure
When a potentiometer is connected between A & B, the balancing length of the potentiometer wire is 300 cm. On connecting the same potentiometer between A & C, the balancing length is 100cm. Calculate the ratio of E1 & E2.
Q15.In a potentiometer, a standard cell of emf 5V & of negligible resistance maintains a steady current through the potentiometer wire of length 5m. Two primary cells of emfs E1 & E2 are joined in series with (i) same polarity & (ii) opposite polarity. The combination is connected through a galvanometer& a jockey to the potentiometer. The balancing lengths in the two cases are found to be 350cm and 50cm respectively.
(i) Draw the necessary circuit diagram.
(ii)Find the value of the emfs of the two cells.
PHYSICS ASSIGNMENT
CLASS – XII
Chapter – 4 :Moving Charges and Magnetism
Theory Based Questions:
Q1.Use BiotSavart’s law to derive an expression for the magnetic field due to circular current carrying loop lying (a) at the centre of the loop, (b) on the axis of the loop.
Q2.State Ampere Circuital Law. Use it to find magnetic field due to
(a)An infinitely long straight current carrying wire,
(b)A solenoid carrying current,
(c)A toroid carrying current.
Q3.Derive a mathematical expression for the force acting on a current carrying conductor kept in a magnetic field. Under what conditions is this force (i) zero and(ii) maximum.
Q4. Deduce an expression for the force between two thin parallel straight conductor carrying current. Hence define one ampere.
Q5. Obtain an expression for the torque acting on a rectangular coil of area A carrying current I placed in a magnetic field B at an angle θ to the direction of the field.
Q6.With the help of a labelled diagram, explain principle, construction, theory and working of a cyclotron. Also write its limitations and uses.
Q7.Describe the construction, principle and working of a moving coil galvanometer. Also derive the necessary mathematical formula. What is the function of radial field and soft iron core in such device?
Q8.When is galvanometer said to be sensitive? Define current sensitivity and voltage sensitivity of a galvanometer. State the factors on which the sensitivity of a moving coil galvanometer depends.
Q9.How can a galvanometer be converted into an ammeter? Support with necessary mathematical expression.
Q10.How can a galvanometer be converted into a voltmeter? Support with necessary mathematical expression.
Numerical Questions
Q1.The magnetic induction at a point P which is at a distance of 4cm from a long current carrying wire is 10-3T. What is the magnetic induction at another point Q which is at a distance of 12 cm from this current carrying wire?
Q2.The magnetic field due to a current carrying circular loop of radius 12 cm at its centre is 0.5 x 10-4T. Find the magnetic field due to this loop at a point on the axis at a distance of 5 cm from the centre.
Q3.A solenoid of length 0.5 m has 500 turns & has a flux density of 2.52 x 10-3T at its centre. Find the current in the solenoid.
Q4.A positive charge of 1.5µC is moving with a speed of 2 x 106 m/s along positive x-axis. A magnetic field =0.2ĵ + 0.4 k̂ Tesla acts in space. Find the magnetic force.
Q5.A cyclotron has an oscillatory frequency of 12MHz and a dee radius of 50 cm. Calculate the magnetic field required to accelerate deuterons of mass 3.3 x10-27kg and charge 1.6 x 10-19C. What is the energy of the deuterons emerging from the cyclotron?
Q6.A horizontal wire 0.1 m long having mass 3 g carries a current of 5A. Find the magnitude of the magnetic field which must act at 300 to the length of the wire in order to support its weight?
Q7.Two straight wires A and B of lengths 10 m and 12 m carrying currents of 4A & 6A respectively in opposite directions, lie parallel to each other at a distance of 3 cm. Estimate the force on a 15 cm section of the wire B near its centre.
Q8.Calculate the torque on a 100 turn rectangular coil of length 40 cm & breadth 20 cm, carrying a current of 10 A, when placed making an angle of 600 with a magnetic field of 3T.
Q9.A galvanometer needs 50 mV for a full scale deflection of 50 divisions. Find its voltage sensitivity. What must be its resistance if its current sensitivity is 1 division/ µA?
Q10.How will you convert 1m A full scale deflection meter of resistance 100 Ω into an ammeter to read 1 A (full scale deflection) and into a voltmeter to read 1 volt (full scale deflection) ?