1.

a) State Biot-Savarts law.

b)

3.

The y - and z-axes, respectively, carry filamentary currents 10 A along ay and

20 A along -az. Find Hat (-3,4,5).

2. A conducting filament carries current I from point A(0, 0, a) to point B(0, 0, b). Show

that at point P(x, y,0),

a) State Ampere's circuit law.

b) A hollow conducting cylinder has inner radius a and outer radius b and carries a

current I along the positive z - direction. Find H everywhere.

4. An infinitely long filamentary wire carries a current of 2 A along the z-axis in the

+z - direction. Calculate the following:

a) B at (-3,4,7)

b) The flux through the square loop described by 2 ≤ p ≤ 6,0 ≤z ≤ 4, = 90°

5. Determine the magnetic flux through a rectangular loop (a × b) due to an infinitely long

conductor carrying current I as shown in Figure 7.1. The loop and the straight conductors

are separated by distance d./nFigure 7.1.- For Problem 5

6. A brass ring with triangular cross section encircles a very long straight wire

concentrically as in Figure 7.2. If the wire carries a current I, show that the total number

of magnetic flux lines in the ring is

4

Molh

2лb

[b-anª+b]

Calculate if a = 30 cm, b = 10 cm, h = 5 cm, and I = 10 A.

Brass ring

Figure 2.- Cross section of a brass ring enclosing a long straight wire; for Problem 6/n7. Consider the following arbitrary fields. Find out which of them can possibly represent an

electrostatic or magnetostatic field in free space.

a) A = y cos ax ax + (y + e¯x)az

20

b)

B=ap

c) C = r² sin a

8. Reconsider Problem 7 for the following fields.

EECE 3101

Homework 5

a) D = y²zax + 2(x + 1)yzay − (x + 1)z²az

b) E=

(z+1)

Р

cos pap + az

sin o

Р

c) F=(2 cos 0 a, + sin 0 a.)

Fall 2023/n9. For a current distribution in free space,

A = (2x²y + yz)ax + (xy² − xz³)ay - (6xyz – 2x²y²)a₂ Wb/m

a) Calculate B

b) Find the magnetic flux through a loop described by x = 1, 0

2

c) Show that V. A = 0 and V. B = 0.

10. The magnetic vector potential of a current distribution in free space is given by

A = 15e º sin pa, Wb/m

Find Hat (3,7/4,-10). Calculate the flux through p = 5,0 ≤ ≤ π/2,0 ≤ z ≤ 10.