PHY2323 – Electricity and Magnetism Assignment 5
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PHY2323 – Electricity and Magnetism
Assignment 5
1. Section 5.6 in the book refers to the Magnetic Vector Potential. The magnetic vector potential, 
, can be defined to simplify the calculation of the magnetic field. We used a similar approach when discussing electrostatics. In chapter 3, we defined the electric potential, V, that was related to the electric field as 
= −
. Now, by defining the magnetic vector potential, 
, we can determine the magnetic flux density by using 
= 
× 
. This can simplify some problems by avoiding having to use the Biot-Savart equation. Your task for this first question is simple: Read section 5.6 of the book about magnetic vector potentials (p.194-196). Understand example 5.9. Finally, when you submit your assignment, write down an expression for 
, as it is presented in this section.
2. The region of space 
< 
(region 1) is filled with a magnetic material with a permeability of 
, while the region 
> 0 (region 2) is air with permeability 
. In the 
< 
region (region 1), the magnetization is uniform and given by 
= 
− 
+ 
(
/
). There is no free current on the interface at x = 0.
a. Find the magnetic field intensity 
in region 1 (x < 0).
b. State the normal and tangential components of 
c. Find the magnetic field intensity 
in region 2 (x > 0).
3. Imagine a solenoid that has a current-carrying wire wrapped around an object with a square cross-section. This solenoid has 150 windings. The sides of the square cross-section of sides 50 cm. You can assume that the diameter of the wire is negligible. This solenoid is exposed to a uniform external field of |
| = 5 
. When the direction of this magnetic flux density makes an angle of 15 degrees with respect to the plane of the solenoid, the measured torque is 60 Newton·Metre. What is the current flowing through this solenoid?
4. An external magnetic flux density 
= (3
− 5
+ 7
) 
exists everywhere. Determine the total magnetic flux passing through the six triangular surfaces of a hexagonal pyramid whose hexagonal base lies in the XY plane and is centered at the origin, and whose apex is located at z = 4 m. The six sides of the hexagonal base have length 2 m. [Hint: This question is easier than you might think…]
5. Two conducting rails lie in the XY plane as shown in blue in the diagram. The two rails have no electrical resistance. An external magnetic field exists and equals 
= (2
+ 3
) 
. A conducting rod (in black) of constant resistance
= 30 Ω slides over the rails towards the right at a constant velocity 
= 3
/
. The angle between the two blue rails is 90o . What is the current
flowing in the closed conducting loop created by this system, as a function of
x and v? Don’t forget to determine the direction of this current.
2022-04-01