Question

A long, hollow, cylindrical conductor (inner radius 2.4 mm, outer radius 4.4 mm) carries a current of 45 A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of 24 A in the opposite direction. What is the magnitude of the magnetic field (a) 1.4 mm, (b) 2.6 mm, and(c) 4.7 mm from the central axis of the wire and cylinder?

Answer 1

Given that :

inner radius of hollow cylinder, a = 2.4 mm

outer radius of hollow cylinder, b = 4.4 mm

current, I = 45 A

Magnitude of the magnetic field at following points :

(a) At r = 1.4 mm

in this case,   r < a

B_r=1.4 = 0

(b) At r = 2.6 mm

in this case,   a r b

using an equation, B_r=2.6 = (₀ I / 2r) [r² - a² / b² - a²]                                                             { eq.2 }

inserting the values in above eq,

B_r=2.6 = [(4 x 10^-7 m.T/A) (45 A) / 2 (2.6 x 10^-3 m)] [(0.0026m)² - (0.0024 m)² / (0.0044 m)² - (0.0024 m)²]

B_r=2.6 = (34.6 x 10^-4 T) (0.0735)

B_r=2.6 = 2.54 x 10^-4 T

(c) At r = 4.7 mm,

in this case, r > b

using an equation, B_r=4.7 = (₀ I / 2r)                                                    { eq.2 }

inserting the values in eq.2,

B_r=4.7 = (4 x 10^-7 m.T/A) (45 A) / 2 (4.7 x 10^-3 m)

B_r=4.7 = (90 x 10^-7 m.T) / (4.7 x 10^-3 m)

B_r=4.7 = 19.1 x 10^-4 T

B_r=4.7 = 1.91 x 10^-3 T