Respuesta :
Answer:
The power must be delivered to the solenoid is 0.253 watt.
Explanation:
Given that,
Diameter = 10.0 cm
Length = 70 .0 cm
Diameter of copper wire = 0.100 cm
Magnetic field = 5.10 mT
We need to calculate the number of turns
[tex]n=\dfrac{l}{d}[/tex]
Where, l = length
d = diameter of copper wire
Put the value into the formula
[tex]n =\dfrac{70.0}{0.100}[/tex]
[tex]n=700[/tex]
We need to calculate the current
Using formula of magnetic field
[tex]B =\dfrac{\mu n i}{l}[/tex]
[tex]i =\dfrac{Bl}{\mu n}[/tex]
Where, B = magnetic field
n = number of turns
l = length
Put the value into the formula
[tex]i =\dfrac{5.10\times10^{-3}\times70.0\times10^{-2}}{4\times3.14\times10^{-7}\times700}[/tex]
[tex]i=4.06\ A[/tex]
We need to calculate the resistance
Using formula of resistance
[tex]R =\dfrac{\rho l}{A}[/tex]
We know ,
The resistivity of the copper wire [tex]\rho=1.72\times10^{-8}\Omega-m[/tex]
Put the value into the formula
[tex]R=\dfrac{1.72\times10^{-8}\times70\times10^{-2}}{3.14\times(\dfrac{0.100}{2}\times10^{-2})^2}[/tex]
[tex]R=0.0153\Omega[/tex]
We calculate the power
Using formula of power
[tex]P = i^2R[/tex]
[tex]P = 4.06^2\times0.0153[/tex]
[tex]P=0.253\ Watt[/tex]
Hence, The power must be delivered to the solenoid is 0.253 watt.
