# magnetism homework help

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• Q1: 2 Consider a current I = 1 A flowing in the positive y direet ion through a rectan-gular conductor as shown in Figure Q2. The conductor has length L = 4 cm,width a = 1 cm, and height b = 0.1 cm. Suppose that a magnetic field B = Bàpermeates uniformly the conductor, with B = 10 T. Briefly explain why a potential difference AV = V - V, arises at the equilibrium between the left and right sides of the conductor, as shown in the figure. Starting from J = n, qữa and considering the Lorentz force, derive the force acting on the carriers responsible for the current I function of the relevant parameters a, b, I, B and the carrier density ng: Use such result to demonstrate that the carriers responsible for the current in the metal are negatively charged if the potential difference measured between the left and the right facets of the conductor is positive:deltaV = V - V, > 0. To this end, consider that V- V, is positive if the carriers accumulated on the right side have a negative charge. Suppose that the carriers are electrons ( -1.6x 10-19 C) and thatAV = V,- V, = 22 x 10-6 V. Caleulate the carrier density ngmetal, expressed in units of m .%3Din the Hence or otherwise, suppose that the current I is induced by a generator keeping the potential difference between the input and and output facets (sand S) at a constant value DElta Vt/0=0.002 V what is the resistivity p of the conductorSee Answer
• Q2: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 ➤XSee Answer
• Q3: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 12See Answer
• Q4: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: ISee Answer
• Q5:Problem 5 [ 17.5] Two identical cube magnets are held on the top of each other at distance D (the distance between the top and bottom face of the two cubes) as shown in the fhgure. The magnetisation of each bar is M - M₂ 5.1 [7/2.5] Find the magnetic surface charge density on each side of the cubes Answer LScore: ? Comment: 5.2 [2/4] Find the magnetic charges on each side the cubes. D y Fig. 5: A magnetic circuit consisting of 4 sections.See Answer
• Q6:5.1 [?/2.5] Find the magnetic surface charge density on each side of the cubes Answer: LScore: ? | Comment: 5.2 [7/1] Find the magnetic charges on each side of the cubes. Answer: LScore: ? | Comment: 5.3 [2/4] Assume that the magnetic charges in 5.2 are point charges. Find the total force (magnitude and direction) on the top magnet due to the bottom magnet. Answer: -Score: ? | Comment:See Answer
• Q7:Problem 3 [13] The loop in the figure below is in the x-y plane and B=2Bcosat +(2x-3y +42) Bosinot with Bo=1.5T, = 2xx 10³ Rad/sr (radius) = 10 cm, and R = 1092. 3.1 [ 3.1 [2/3] Find the induce current and its direction (clockwise or anticlockwise when viewing the loop from the above) at: (a) - 0 (b) axt= (c) ax = emf Fig. 3: A loop is located in the x-y plane and connected to a resistor.See Answer
• Q8: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]See Answer
• Q9:An air core transmission line has an inner hollow tube conductor of radius b and a very thin outer conductor of inner radius a. Determine the inductance of the line if its length is L (La). (Approx. 5 min.) (HoL/2x) In a/b Ho/4x + (Ho/n) In a/b None of them. HoL/8+ (μL/2n) In a/b (HZ/2x) In bla MoL/8x + (HoL/2n) In bla (μ/2x) In a/b Ho/8x + (Ho/2n) In a/bSee Answer
• Q10:Q4 A very long solenoid having n turns per unit length has radius a. The permeability of the core is . If the magnetic energy density inside of the solenoid is (un²/2), determine the stored magnetic energy per unit length of the solenoid. (Approx. 5 min.) ooooooo un²12²πa²/4 None of them. u²n² 1²πa²/2 нп2 1 па2 un²²πa³/3 u² n² 1² m² a²/2 μn/ma/2 μ²n² 1²πa²/4 HN2 12 пLa2/2See Answer
• Q11: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.See Answer
• Q12: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 conductorSee Answer
• Q13: . 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. See Answer
• Q14: Use macroscopic Ohm's and Kirchhoff's laws to demonstrate that thetotal resistance of two resistors connected in series in a eircuit equatesthe sum of their resistance.[6] Use macroscopic Ohm's and Kirchhoff's laws to demonstrate that thetotal resistance R of two resistors of resistance R and R2 connected 5]in parallel is R = (R'+ R'). Calculate the total capacitance C that two capacitors with capacitanceC1 = 1 pF and C, = 2 pF introduce in a circuit if they are connected in series. Calculate the total capacitance C that two capacitors with capaci-tance C = 11 pF and C = 22 p F introduce in a circuit if they are connected in parallel.See Answer
• Q15: . A simple atom has a ground state |g) and an excited state |e), with energies E, :E = E, respectively.= 0 and (a) Draw the energy level diagram, and label all relevant aspects. (b) The atom is prepared in the state |\psi\rangle=\sqrt{\frac{2}{3}}|g\rangle+\sqrt{\frac{1}{3}}|e\rangle Calculate the probability of finding the atom in the excited state Je). (c) Calculate the expectation value for the energy of the atom in state psi The time evolution of the atom is governed by the Hamiltonian H, with H=E_{g}|g\rangle\left\langle g\left|+E_{e}\right| e\right\rangle\langle e| Calculate the state of the atom at time t = T, given that the atom is in state |) at time t = 0. At time T we measure whether the atom is in the state |+\rangle=\frac{|g\rangle+|e\rangle}{\sqrt{2}} \quad \text { or } \quad|-\rangle=\frac{|g\rangle-|e\rangle}{\sqrt{2}} Calculate the probability of finding the atom in state |+), and sketch this probability as a function of time.See Answer
• Q16: 1) For the lab-1 and lab-2 online what are the dependent, independent and control variablesSee Answer
• Q17: 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 positionedSee Answer
• Q18: 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?See Answer
• Q19: (a) The temperature coefficient of resistivity of copper is 3.9 x 103K. The resistivity of copper1 mm is heated to 80°C.1.72 x 10-8 m at 20°C. A copper wire of length 10 cm and diameter i. Calculate the resistivity of copper at 80°C. ii. The wire is connected to a battery providing a voltage of 1.5 V. Calculate the power dissipated in the wire. A sphere of radius R carries a charge density \rho(r)=\frac{5 Q r^{2}}{4 \pi R^{5}} where r is the radial distance from the centre of the sphere. i. Sketch the charge densityas a function of r from r = 0 to r = 2R. ii. Show that the total charge of the sphere is Q. iii. Calculate the electric field E inside the sphere. iv. Calculate the electric field outside the sphere. v. Sketch the electric field magnitude as a function of r from r = 0 to r = 2R.See Answer
• Q20: Consider a region of space free from matter and from magnetic fields.Show that it cannot be permeated by an electric field of the form: \vec{E}(x, y, z)=\frac{A}{2}(y \hat{x}-x \hat{y}+z \hat{z}) where A is a constant value different from zero and with units V/m2. Now, consider that a magnetic field permeates the region of(a). Write an expression representing a time-varying magnetic field B(r,y, z, t) that renders the vector field proposed in (a) suitable to describe an electric field. Check and demonstrate that the expression you found is a suitable representation of a magnetic field. Hence or otherwise, show that: \vec{B}=K x \hat{x}+K y \hat{y}+A t \hat{z} is not an adequate expression for a magnetic field for K # 0 T/m2.See Answer

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