PHY3401 Assignment 5 July 2006 Semester 1. (a) State Biot-Savart’s law.

(b) The y- and z-axes, respectively, carry filamentary currents 10 A along xa and 20 A along za− . Find H at ( 3, 4, 5)− .

(Sadiku Problem 7.1) 2. An infinitely long conductor is bent into an L shape as shown below. If a direct

current of 5 A flows in the current, find the magnetic field intensity at (a) (2, 2, 0)

x 5 A

y (b) (0, 2, 0)−(c) (0, 0, 2)(Sadiku Problem 7.7)

5 A

3. A solenoid of radius 4 mm and length 2 cm has 150 turns/m and carries current . Find 500 mA

(a) H at the center;

(b) H at the ends of the solenoid. (Sadiku Problem 7.15)

4. (a) State Ampere’s circuit law.

(b) A hollow conducting cylinder has inner radius a and outer radius b and carries current I along the positive z-direction. Find H everywhere.

(Sadiku Problem 7.17) 5. An infinitely long filamentary wire carries a current of 2 A in the +z-direction.

Calculate (a) B at ( 3, 4, 7)−(b) the flux through the square loop described by 2 6ρ≤ ≤ , 0 4z≤ ≤ ,

90φ = ° . (Sadiku Problem 7.21)

6. The magnetic vector potential of a current distribution in free space is given by 15 sin Wb/m .zA e aρ φ−=

Find H at (3, / 4, 10)π − . Calculate the flux through 5ρ = , 0 / 2φ π≤ ≤ , . 0 1z≤ ≤ 0

(Sadiku Problem 7.29)

7. Find the current density J to

2

10 Wb/mzA aρ

=

in free space. (Sadiku Problem 7.33)

8. Plane carries a current of 2z = − 50 A/mya . If 0mV = at the origin, find at mV

(a) ( 2, 0, 5)−(b) (10, 3,1)(Sadiku Problem 7.37)

9. An electron with velocity 5(3 12 4 ) 10 m/sx y zu a a a= + − × experiences no net

force at a point in a magnetic field 210 20 30 mWb/mx y zB a a a= + + . Find E at that point. (Sadiku Problem 8.1)

10. A particle with mass 1 kg and charge 2 C starts from rest at point in a

region where (2, 3, 4)−

4 V/myE a= − and 25 Wb/mxB a= . Calculate (a) the location of the particle at 1st = ; (b) its velocity and kinetic energy at that location; (Sadiku Problem 8.3)

11. A current element of length 2 cm is located at the origin in free space and carries

current 12 mA along xa . A filamentary current of 15 za is located along , . Find the force on the current filament.

3x =4y =

(Sadiku Problem 8.7) 12. In a certain material for which 06.5µ µ= , 10 25 40 A/m ,x y zH a a a= + −

find (a) the magnetic susceptibility mχ of the material; (b) the magnetic flux density B ; (c) the magnetization M ; (d) the magnetic energy density. (Sadiku Problem 8.17)

13. If 1 2 0µ µ= for region 1 (0 )φ π< < and 2 5 0µ µ= for region 2 ( 2 )π φ π< <

and 22 10 15 20 mWb/mzB a a aρ φ= + − . Calculate:

(a) 1B ; (b) the energy densities in the two media.

(Sadiku Problem 8.23) 14. The interface between two magnetic media carries current 4 5 0x z− = 35

A/m. If ya

1 25 30 45 A/mx y zH a a a= − + in the region 4 5 0x z− ≤ where

1 5rµ = , calculate 2H in region 4 5 0x z− ≥ where 2 10rµ = . (Sadiku Problem 8.25)

15. The core of a toroid is 12 and is made of material with 2cm 200rµ = . If the mean radius of the toroid is 50 cm, calculate the number of turns needed to obtain an inductance of 2.5 . H(Sadiku Problem 8.33)

16. A toroid with air gap shown in Figure below, has a square cross section. A long

conductor carrying 2I is inserted in the air gap. If 1 200 mAI = , , 750N =

0 10 cmρ = , , and l5 mma = 1 mma = , calculate (a) the force across the gap when 2 0I = and the relative permeability of the toroid

is 300; (b) the force on the conductor when 2 2 mAI = and the permeability of the toroid is

infinite. Neglect fringing in the gap in both cases. (Sadiku Problem 8.41)

X

N

aρ 0

I2

I1

la