Respuesta :
Answer with Explanation:
We are given that
Resistivity of copper wire=[tex]\rh0=1.68\times 10^{-8}\Omega m[/tex]
Diameter=d=[tex]1.00\times 10^{-3} m[/tex]
Radius of copper wire=[tex]r=\frac{d}{2}=\frac{1}{2}\times 10^{-3} m[/tex]
Radius of solenoid=r'[tex]=3 cm=3\times 10^{-2} m[/tex]
1 m=100 cm
a.Length of wire=l=11.3 m
Area of wire=A=[tex]\pi r^2[/tex]
Where [tex]\pi=3.14[/tex]
A=[tex]3.14\times (\frac{1}{2}\times 10^{-3})^2[/tex]
Resistance, R=[tex]\rho \frac{l}{A}[/tex]
Using the formula
[tex]R=1.68\times 10^{-8}\times\frac{11.3}{3.14\times (\frac{1}{2}\times 10^{-3})^2}[/tex]
[tex]R=0.24\Omega[/tex]
B.Length of solenoid=[tex]2\pi r'=2\times 3.14\times 3\times 10^{-2}=0.188[/tex] m
Number of turns=[tex]n_0=\frac{l}{2\pi r'}=\frac{11.3}{0.188}[/tex]
[tex]n_0[/tex]=60
C.Potential difference,V=3 V
Current,I=[tex]\frac{V}{R}[/tex]
I=[tex]\frac{3}{0.24}=12.5 A[/tex]
D.Total length =0.1 m
Number of turns per unit length,n=[tex]\frac{60}{0.1}=600[/tex]
Magnetic field along central axis inside of the solenoid,B=[tex]\mu_0 nI[/tex]
[tex]B=4\pi\times 10^{-7}\times 12.5\times 600=9.42\times 10^{-3} T[/tex]
Answer:
Explanation:
resistivity of copper, ρ = 1.68 x 10^-8 ohm - m
diameter = 1 x 10^-3 m
radius of wire, r = 0.5 x 10^-3 m
Radius of solenoid, r' = 3 cm
(A)
Length of wire, l = 11.3 m
Let the resistance of wire is R.
[tex]R= \frac{\rho\times l}{A}[/tex]
where, A is the crossection of wire
A = 3.14 x 0.5 x 10^-3 x 0.5 x 10^-3 = 7.85 x 10^-7 m²
[tex]R= \frac{1.68\times 10^{-8}\times 11.3}{7.85\times 10^{-7}}[/tex]
R = 0.24 ohm
(B)
Let the number of turns is N.
Length of wire = N x circumference of one turn
11.3 = N x 2 x 3.14 x 0.03
N = 60
(C)
V = 3 V
R = 0.24 ohm
V = i x R
3 = i x 0.24
i = 12.5 A
(D) number of turns per unit length, n = N / 0.1 = 60 / 0.1 = 600
The magnetic field is given by
[tex]B = \mu _{0}ni[/tex]
[tex]B = 4 \times 3.14 \times 10^{-7}\times 600\times 12.5[/tex]
B = 9.42 x 10^-3 Tesla
