Respuesta :
Answer:
Part a)
[tex]N = 754 turns[/tex]
Part b)
[tex]L = 0.376 m[/tex]
Explanation:
Resistance of the solenoid is given as
R = 4.10 ohm
now we have
[tex]R = \rho \frac{L}{A}[/tex]
here we know that
[tex]\rho = 1.7 \times 10^{-8} ohm-m[/tex]
[tex]A = \pi r^2 = \pi (\frac{0.5 \times 10^{-3}}{2})^2[/tex]
[tex]A = 1.96 \times 10^{-7} m^2[/tex]
now from above formula
[tex]4.10 = (1.7 \times 10^{-8})\frac{L}{1.96 \times 10^{-7}}[/tex]
[tex]L = 47.35 m[/tex]
Part a)
now we know that it is wounded over the solenoid
so here we can say
[tex]N(2\pi R) = L[/tex]
[tex]N(2 \pi (0.01)) = 47.35[/tex]
[tex]N = 754 turns[/tex]
Part b)
now length of solenoid is given as
[tex]L = N(diameter\: of\: the\: wire)[/tex]
[tex]L = 754(0.5 \times 10^{-3})[/tex]
[tex]L = 0.376 m[/tex]
Answer:
(a) 753.68
(b) 9.35 cm
Explanation:
R = 4.1 ohm
B = 4 x 10^-2 T
i = 3.95 A
diameter of copper wire = 0.5 mm
radius of copper wire, r = 0.5 / 2 = 0.25 mm = 0.25 x 10^-3 m
Radius of solenoid, R = 1 cm = 0.01 m
Resistivity of copper, ρ = 1.7 x 10^-8 ohm - m
(a) Let N be the total number of turns
use the formula for the resistance
Let L be the length of wire
R = ρ L / A
L = R x A / ρ = (4.10 x 3.14 x 0.25 x 10^-3 x 0.25 x 10^-3) / (1.7 x 10^-8)
L = 47.33 m
N = L / 2 π R = 47.33 / ( 2 x 3.14 x 0.01) = 753.68
(b) Let the length of the solenoid is L'
So, n = N / L' = 753.68 / L'
B = μo x n x i
4 x 10^-2 = 4 x 3.14 x 10^-7 x 753.68 x 3.95 / L'
4 x 10^-2 = 3.74 x 10^-3 / L'
L' = 0.0935 m = 9.35 cm
