# Magnetism

(Please refer to the attachment for detailed description of the problems)

4. The figure shows a circular region of radius R = 3.00 cm in which a uniform displacement current id = 0.500 A is directed out of the page.

(a) What is the magnitude of the magnetic field due to the displacement current at a radial distance of 2.00 cm?

(b) What is it at a radial distance of 5.00 cm?

5. Assume the average value of the vertical component of Earth's magnetic field is 53 µT (downward) over an area of 3.25 10^5 km^2. What then are the (a) magnitude and (b) direction (inward or outward) of the net magnetic flux through the rest of Earth's surface (the entire surface excluding this area)?

6. An electron is placed in a magnetic field that is directed along a z axis. The energy difference between parallel and antiparallel alignments of the z component of the electron's spin magnetic moment with is 4.7 10^-25 J. What is the magnitude of ?

7. A magnet in the form of a cylindrical rod has a length of 4.70 cm and a diameter of 1.20 cm. It has a uniform magnetization of 4.90 10^3 A/m. What is its magnetic dipole moment?

8. The magnitude of the dipole moment associated with an atom of iron in an iron bar is 2.1 10^-23 J/T. Assume that all the atoms in the bar, which is 4.0 cm long and has a cross-sectional area of 1.2 cm^2, have their dipole moments aligned.

(a) What is the dipole moment of the bar?

(b) What torque must be exerted to hold this magnet perpendicular to an external field of 1.3 T? (The density of iron is 7.9 g/cm3.)

9. The saturation magnetization Mmax of a ferromagnetic metal is 4.10 10^5 A/m. Calculate the magnetic dipole moment of a single atom of this metal. (The density of the metal is 8.85 g/cm3, and its molar mass is 60.94 g/mol.)

10. Measurements in mines and boreholes indicate that Earth's interior temperature increases with depth at the average rate of 30 degree C/km. Assuming a surface temperature of 10 degree C, at what depth does iron cease to be ferromagnetic? (The Curie temperature of iron varies very little with pressure.)

#### Solution Preview

Please refer to the attachment.

4.

Uniform displacement current. The figure below shows a circular region of radius R = 3.00 cm in which a uniform displacement current id = 0.500 A is directed out of the page.

(a) What is the magnitude of the magnetic field due to the displacement current at a radial distance of 2.00 cm?

µT

(b) What is it at a radial distance of 5.00 cm?

µT

Solution: Density of the displacement current with in the circular region = Jd = Id/ПR2 = 0.5/Пx0.032 = 176.93 A/m2

B

2cm 3cm B

B

B

As per Ampere Maxwell law: ∫B . dl = μo(I + Id) where Id is the displacement current

a) We consider an Amperian loop of radius 2 cm and apply the Ampere Maxwell law to the same.

As there is no conduction current, I = 0

Displacement current enclosed by the Amperian loop = Jd x П x r2 = 176.93 x П x 0.022 = 0.22 A

∫B . dl = B (2П x 0.02) = 4П x 10-7 x 0.22

B = (4П x 10-7 x 0.22)/(2П x 0.02) = 22 x 10-7 T or 2.2 μT

b) For radial distance of 5 cm, Id = 0.5 A.

∫B . dl = B (2П x 0.05) = 4П x 10-7 x 0.5

B = (4П x 10-7 x 0.5)/(2П x 0.05) = 20 x 10-7 T or 2 μT

5.

Assume the average value of the vertical component of Earth's magnetic field is 53 µT (downward) over an area of 3.25 105 ...

#### Solution Summary

The expert examines magnetism circular region displacement. The radical distance is calculated.