Electric And Magnetic Phenomena Assignment

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 density ?

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 , 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 ? J 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 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.

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