Answer:
a) Фm = μ₀*I*n*π*N*R₁²
b) Фm = μ₀*I*n*π*N*R₂²
Explanation:
Given
n = number of turns per unit length of the solenoid
R₁ = radius of the solenoid
I = current passing through the solenoid
R₂ = radius of the circular coil
N = number of total turns on the coil
a) Фm = ? If R₂ > R₁
b) Фm = ? If R₂ < R₁.
We can use the formula
Фm = N*B*S*Cos θ
where
N is the number of turns
B is the magnetic field
S is the area perpendicular to magnetic field B.
The magnetic field outside the solenoid can be approximated to zero. Therefore, the flux through the coil is the flux in the core of the solenoid.
We know that the magnetic field inside the solenoid is uniform. Thus, the flux through the circular coil is given by the same expression with R2 replacing R1 (from the area).
a) Then, the flux through the large circular loop outside the solenoid (R₂ > R₁) is obtained as follows:
Фm = N*B*S*Cos θ
where
B = μ₀*I*n
S = π*R₁²
θ = 0°
⇒ Фm = (N)*(μ₀*I*n)*(π*R₁²)*Cos 0°
⇒ Фm = μ₀*I*n*π*N*R₁²
b) The flux through the coil when R₂ < R₁ is
Фm = (N)*(μ₀*I*n)*(π*R₂²)*Cos 0°
⇒ Фm = μ₀*I*n*π*N*R₂²
Answer:
The velocity of the wave is, v = 180,000 m/s
Explanation:
Given data,
The frequency of the wave, f = 900 Hz
The wavelength of the wave, λ = 200 m
The formula for the speed of the wave when the frequency and wavelength are known,
v = λ x f
Substituting the given values in the above equation,
v = 200 m x 900 Hz
v = 180000 m/s
Hence, the velocity of the wave is, v = 180,000 m/s
Answer:
kinetic energy = 20 J
Explanation:
KE = ½mv²
= ½× <u>100 </u> × 20 × 20
1000
KE = 20 J//
Answer:
![T=51.64^\circ F](https://tex.z-dn.net/?f=T%3D51.64%5E%5Ccirc%20F)
![t=180.10s](https://tex.z-dn.net/?f=t%3D180.10s)
Explanation:
The Newton's law in this case is:
![T(t)=T_m+Ce^{kt}](https://tex.z-dn.net/?f=T%28t%29%3DT_m%2BCe%5E%7Bkt%7D)
Here,
is the air temperture, C and k are constants.
We have
in
So:
![T(0)=70^\circ F\\T(0)=10^\circ F+Ce^{k(0)}\\70^\circ F=10^\circ F+C\\C=70^\circ F-10^\circ F=60^\circ F](https://tex.z-dn.net/?f=T%280%29%3D70%5E%5Ccirc%20F%5C%5CT%280%29%3D10%5E%5Ccirc%20F%2BCe%5E%7Bk%280%29%7D%5C%5C70%5E%5Ccirc%20F%3D10%5E%5Ccirc%20F%2BC%5C%5CC%3D70%5E%5Ccirc%20F-10%5E%5Ccirc%20F%3D60%5E%5Ccirc%20F)
And we have
in
, So:
![T(30)=60^\circ F\\T(30)=10^\circ F+(60^\circ F)e^{k(30)}\\60^\circ F=10^\circ F+(60^\circ F)e^{k(30)}\\50^\circ F=(60^\circ F)e^{k(30)}\\e^{k(30)}=\frac{50^\circ F}{60^\circ F}\\(30)k=ln(\frac{50}{60})\\k=\frac{ln(\frac{50}{60})}{30}=-0.0061](https://tex.z-dn.net/?f=T%2830%29%3D60%5E%5Ccirc%20F%5C%5CT%2830%29%3D10%5E%5Ccirc%20F%2B%2860%5E%5Ccirc%20F%29e%5E%7Bk%2830%29%7D%5C%5C60%5E%5Ccirc%20F%3D10%5E%5Ccirc%20F%2B%2860%5E%5Ccirc%20F%29e%5E%7Bk%2830%29%7D%5C%5C50%5E%5Ccirc%20F%3D%2860%5E%5Ccirc%20F%29e%5E%7Bk%2830%29%7D%5C%5Ce%5E%7Bk%2830%29%7D%3D%5Cfrac%7B50%5E%5Ccirc%20F%7D%7B60%5E%5Ccirc%20F%7D%5C%5C%2830%29k%3Dln%28%5Cfrac%7B50%7D%7B60%7D%29%5C%5Ck%3D%5Cfrac%7Bln%28%5Cfrac%7B50%7D%7B60%7D%29%7D%7B30%7D%3D-0.0061)
Now, we have:
![T=10^\circ F+(60^\circ F)e^{-0.0061t}(1)](https://tex.z-dn.net/?f=T%3D10%5E%5Ccirc%20F%2B%2860%5E%5Ccirc%20F%29e%5E%7B-0.0061t%7D%281%29)
Applying (1) for
:
![T=10^\circ F+(60^\circ F)e^{-0.0061*60}\\T=10^\circ F+(60^\circ F)0.694\\T=10^\circ F+41.64^\circ F\\T=51.64^\circ F](https://tex.z-dn.net/?f=T%3D10%5E%5Ccirc%20F%2B%2860%5E%5Ccirc%20F%29e%5E%7B-0.0061%2A60%7D%5C%5CT%3D10%5E%5Ccirc%20F%2B%2860%5E%5Ccirc%20F%290.694%5C%5CT%3D10%5E%5Ccirc%20F%2B41.64%5E%5Ccirc%20F%5C%5CT%3D51.64%5E%5Ccirc%20F)
Applying (1) for
:
![30^\circ F=10^\circ F+(60^\circ F)e^{-0.0061t}\\30^\circ F-10^\circ F=(60^\circ F)e^{-0.0061t}\\-0.0061t=ln(\frac{20}{60})\\t=\frac{ln(\frac{20}{60})}{-0.0061}=180.10s](https://tex.z-dn.net/?f=30%5E%5Ccirc%20F%3D10%5E%5Ccirc%20F%2B%2860%5E%5Ccirc%20F%29e%5E%7B-0.0061t%7D%5C%5C30%5E%5Ccirc%20F-10%5E%5Ccirc%20F%3D%2860%5E%5Ccirc%20F%29e%5E%7B-0.0061t%7D%5C%5C-0.0061t%3Dln%28%5Cfrac%7B20%7D%7B60%7D%29%5C%5Ct%3D%5Cfrac%7Bln%28%5Cfrac%7B20%7D%7B60%7D%29%7D%7B-0.0061%7D%3D180.10s)