The figure below shows a long conducting coaxial cable and gives its radii (R₁

A hollow spherical conductor of internal radius R2 and external radius R3surrounds a conductive sphere of radius R1, which is charged with a charge Q,as shown in Figure Q1. Derive the expression for the magnitude of the electric field E(r), for between 0 and infinity. Note that r =reference system, as shown in Figure 01.0 is the origin of the spherical Hence or otherwise derive the expression for the scalar potential v(r) for r between 0 and infinity Give a qualitative graphical representation for the functions E(r)(magnitude of the electric field) and V(r) (scalar potential), consid-ering R1 = 30 cm, R2 = 50 cm, R3 = 80 cm, and QUse the appropriate units on the graphs. Write the values of the elec-tric field in the dielectric side of the interface for each of the metallic800 x 10-12 C.%3Dsurfaces. Write the values for the potential at r = 0, r = R1, r = R2,and r = R3. Briefly describe what happens to the scalar potential and electric field in the region with R <r < R2 at the static equilibrium if a charged sphere of radius R,close to the hollow conductor, with its centre at R = 4 m. Include a brief explanation for your answer.= 20 cm and charge Q, = 10-6 C is positioned

Question 1 A long straight, nonmagnetic conductor of 0.2 mm radius carries a uniformly distributed current of 2 A dc. (a) Find J within the conductor (b) Use Ampère's circuital law to find H and B within the conductor (c) Show that V x H = J within the conductor (d) Find H and B outside the conductor. (e) Show that V x H = J outside the conductor

. A circular coil of radius a with N turns lies in the xy plane with the z axis through itscentre, as shown in Fig. 1. The magnetic field along the axis is given by: B(z)=\frac{\mu_{0} N I a^{2}}{2\left(a^{2}+z^{2}\right)^{3 / 2}} :0.20 A, andN =5.0 x 10-Am2 lies along the z axis at a distance of zwhere I is the current. The coil has a =1.0 cm, I =1000. A magneticdipole with magnitude m =+5.0 cm from the centre of the coil. The dipole points along the +z axis. (a) What is the torque on the dipole? (b) What is the magnetic energy of the dipole? (c) What is the force on the dipole? (Hint: make the approximation z? > a².) Byconsidering the coil as a dipole, and making the analogy with bar-magnet dipoles,explain the sign of the force on the dipole. (d) Sketch the dipole's magnetic energy as a function of z, and describe its motion, as-suming that it is free to move without any frictional forces. (Hint: make an analogywith a ball rolling on a curved surface, and apply conservation of energy.) (e) The dipole has a mass of 7.9 x 10-6 kg. What is its maximum speed? (f) The dipole is made of ferromagnetic iron, which has a relative atomic mass of 55.8.Calculate the average dipole moment per iron atom along the z axis in units of theBohr magneton, UB. Explain how this value can be significantly less than uB, eventhough each individual iron atom has a dipole moment of - pg.

QUESTION 2 (a) With the aid of diagrams, differentiate linear polarization from circular polarization. (b) Derive the general equation for electromagnetic wave from Maxwell's equations. (c) A bar magnet is moved rapidly toward a 40-turn circular coil of wire. As the magnet moves, the average value of Bcose over the area of the coil increase from 0.0125T to 0.45 T in 0.250 s. If the radius of the coils is 3.05 cm, and the resistance of its wire is 3.55 2, find the magnitude of (a) the induced emf and (b) the induced current.

4. (5 point) An infinitely-long cylindrical wire with radius a is made of perfect conductor and is located above a perfect conducting ground plane. If the distance between the center of the wire and the ground plane is 2a, then what is the unit capacitance between the wire and the ground?

The figure below shows two wires, each carrying a current. The first wire consists of o circular arc of radius R = 2.8m and two equal radial lengths of L=0.75R; it carries current I₁ = 27A. The second wire is long and straight; it carriers current I2 = 25A, and it is at distance d=0.5R from the center of the arc. At the instant shown a snapshot of a charged particle q moving at velocity v (7.8i +8.9j)m/s toward the straight wire. Find the magnitude of the magnetic force on the charged particle due to the wires in terms of quo. Express your final result using one decimal place. = 4. Z y Answer: >X L L R 45⁰ d 12

Evaluate the magnitude of the net magnetic force on a current loop of 1₁ = 8R, l2 = 6.3R, and r = 7.1R in an external magnetic field B = 7B₂(−î) in terms of B.RI. Express your answer using two decimal places. Please note that a current of 41 runs on the wire. Answer: 1₂ r Ꮎ B 41 4₁ ➤X

The figure below shows a long conducting coaxial cable and gives its radii (R₁ = 2.5cm, R₂=8.3cm, R3-15.2cm). The inner cable has a uniform current density of J = 1.2 A/m², and the outer cable carries a uniform current I = 3.4A flowing in opposite direction. Assume that the currents in each wire is uniformly distributed over its cross section. Determine the magnitude of the magnetic field in terms of Ho at a distance r = 20.3cm from the center of the cable. Express your answer using two decimal places. R R2 R3 Answer: I

Suppose you want to tune in to a radio station such as 91X. They broadcast at a frequency of 91.1 MHz. Assume you have an antenna that is designed to capture this frequency attached to an LRC tuning circuit. Assume your antenna + tuning circuit has a resistance of 75 02, and an inductance of 33nH. a. What is the angular frequency of 91X's broadcast? b. What will make the signal "louder?" (i.e. What exactly do we read out on a receiving antenna?) b. What will make the signc. What capacitance should you tune your adjustable capacitor to in order to hear the radio station clearly d. Why should wap other with a tuning circuit at all?

lo a y The segment of conductor carries current l, = 6 mA and includes a circular arc (symmetric with respect to the y-axis) with radius of a = 0.5 cm and having angle = 60°. What is the magnitude of the magnetic field (A/m) at P (everywhere is air-filled)? [JUST UPLOAD THE ASNWER - NOT SOLUTION]