Reference no: EM131155234
Question 1. A circular current loop of radius a carries a current I Amperes. The magnetic field at point P located a distance z above the center of the disk can be found from the Law of Biot-Savart:
B→ = μ0/4Π∫Idl→ x αˆR/R2
where dl→ = adΦαˆΦ.
(a) Write the unit vector fin from dl→ to P.
(b) Calculate Idl→ x αˆR. What term goes to zero due to symmetry?
(c) Showing all work, calculate the magnetic flux density (including units) B→ at P, and the flux density when z >> a. (Note that z ≠ ∞ so you cannot say B = 0.) Use back of page if necessary.
Question 2.The current in the circuit below is I. What is the value of the integral ∫H→.dl→ calculated around the closed loops A, B, C and D?
Question 3. The diagram below shows the trajectory of a positive charge +q in a crossed electric and magnetic field. Determine the direction of the electric and magnetic fields. Note that the charge is initially at rest at the origin.
Question 4. A wire of radius a =1 mm, length I = 100 meters, and conductivity σ = 5 x 107 Siemans/m is connected to a battery of 10 volts. The wire is oriented in the a^z direction.
(a) Including units, calculate the electric field E→ in the wire, and the resistance R of the wire.
(b) Including units, calculate the total current I and the current density J→
(c) If the number density of charge carriers is N = 5 x1028 per m3 and the charge is 1.602x 10-19 Coulombs, calculate the drift velocity of the charge carriers.
(d) Calculate the magnetic field intensity H→(p) inside the wire (p < a) and outside the wire (p > a). (You can leave answer in terms of p and a.) Plot the field intensity field H vs. p. Use back of page if necessary
Question 5. A ferromagnetic toroid with relative permeability μr = 250 is shown below. The toroid has a .5 cm gap. The radius of the toroid is 12 cm, the cross sectional-area is 8 cm2, and the core is wrapped with N windings carrying 100 mA.
Draw the equivalent circuit and calculate the total magnetic reluctance R.
Calculate the number of turns required to support a flux density of 1.5 Tesla in the air gap (neglecting fringing). Use back of page if necessary.
Question 6. The magnetic vector potential in free space (μ = μo) A→ is
A→ = μ0 (xya^x, -y2a^y -xza^z)
(a) Determine the magnetic flux density B→ (including units).
(b) Determine the volume current density J→ (including units).
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