IGNOU PHE-07 - Electric and Magnetic Phenomena

1. a) What do you understand by electrostatic potential energy? Calculate the electrostatic potential energy for the system of charges shown below. Take q = 5 μC and a = 2 cm. b) A 100 m long thread carries charges uniformly distributed along its length. An electron, 10 cm away from the centre of the thread along a line perpendicular to the thread experiences an attractive force of 2.7 × 10-12N. Calculate the total charge on the thread. c) Consider the figure given below. Charges q1, q2 and q3 are placed at P, Q and R, respectively, and q1 = q2 = -q3  2μC. Determine the magnitude and the direction of the electric field at point A. 2. a) The capacitance of a parallel plate capacitor is increased by a factor of 6 when a dielectric material fills the space between its plates. What is the relative permitivity of the dielectric material? If this material is placed in between the plates of a cylindrical capacitor of outer and inner radii 12 cm and 10 cm respectively, calculate the capacitance per unit length of the cylindrical capacitor. b) A glass of relative permittivity 5 is kept in an external electric field of magnitude 102 Vm-1 . Calculate the polarisation vector, molecular/atomic polarisability and the refractive index of the glass. 3. a) A copper wire of diameter 2 mm and length 30 m is connected across a battery of 2V. Calculate the current density in the wire and drift velocity of the electrons. The resistivity of copper is 1.72 × 10–8 Ωm and n = 8.0 × 1028 electrons m-3. b) A 10 eV electron is circulating in a plane at right angles to a uniform magnetic field of 1.0 × 10–4 T. Calculate the orbital radius of the electron, cyclotron frequency, period of revolution, and the direction of circular motion of the electron as viewed by an observer looking along the magnetic field. c) How do we differentiate between diamagnetic and paramagnetic materials? Show that for diamagnetic atoms placed in an external magnetic field B, the change in dipole moment is opposite to the direction of B. d) Establish the relation B = μ0 (H + M) for a ferromagnetic material. 4. a) An electric generator comprises a square wire loop of side 80 cm. The loop has 50 turns and is placed in a magnetic field of 0.5 T. By what frequency should this loop be rotated in the magnetic field to produce an AC voltage of peak value 250 V? b) Explain the physical significance of the Maxwell’s equation Derive the wave equation for the z-component of the electric field of an electromagnetic wave. c) A sinusoidal plane electromagnetic wave propagates from water (nw =1.33) to glass (ng = 1.5). Calculate the reflection and transmission coefficients for this wave at the interface of the two media. Show that when an electromagnetic wave enters from one dielectric medium to the other, its frequency remains unchanged.

1. a) Determine the electrostatic force and electrostatic field on a charged particle located at A in the Figure given below due to the charged particles situated at B and C. The value of the charge on each of these particles is indicated in the Figure below: Express your result both in the unit vector notation and as magnitude. b) Explain with the help of diagrams what spherically and cylindrically symmetric charge distributions are. What is the electric field at a point inside a hollow metallic sphere of radius R having volume charge densityρ? c) Two particles carrying 4C and - 2C charges are placed on a 1 m long straight wire. Determine the point on the line joining these particles where the electric potential is zero with reference to the positively charged particle. 2. a) Explain the phenomenon of polarisation of a dielectric. Show that, when a dielectric material is filled between the plates of a capacitor, the value of capacitance increases by factor of K, the dielectric constant of the material. b) Determine the value of equivalent capacitance between points A and B for the combination of capacitors shown in the Figure below: c) The energy of a capacitor is 4.0 μJ after it has been charged by a 1.5 V battery. Calculate its energy when it is charged by a 6.0 V battery. 3. a) Obtain an expression to show that the change in the quantity of charge enclosed in an arbitrary volume is accompanied by a net flow of charge inwards or outward across the surface of the enclosed volume. b) A horizontal, straight wire carrying 12.0 A current from west to east is in the earth’s magnetic field B. At this place, B is parallel to the surface of the earth, points to the north and its magnitude is 0.04 mT. Determine the magnetic force on 1 m length of the wire. If mass of this length of wire is 50 g, calculate the value of current in the wire so that its weight is balanced by the magnetic force. c) A current is flowing in an infinitely long straight wire. Using Biot-Savart law, show that the resultant magnetic field at a point along a line perpendicular to the wire is inversely proportional to the distance of the point from the wire. 4. a) Using Maxwell’s equations in free space, derive the wave equation for the electric and magnetic field vectors. b) A uniform plane wave of 100 kHz travelling in free space strikes a large block of a material having ε = 9 ε0, μ = 4 μ0 and σ = 0 normal to the surface. If the incident electric field vector is given by write the complete expressions for the incident, reflected, and transmitted field vectors.