Answer:
(a) The magnetic energy density in the field is 6.366 J/m³
(b) The energy stored in the magnetic field within the solenoid is 5 kJ
Explanation:
magnitude of magnetic field inside solenoid, B = 4 T
inner diameter of solenoid, d = 6.2 cm
inner radius of the solenoid, r = 3.1 cm = 0.031 m
length of solenoid, L = 26 cm = 0.26 m
(a) The magnetic energy density in the field is given by;
![u _B = \frac{B^2}{2\mu_o} \\\\u _B = \frac{(4)^2}{2(4\pi*10^{-7})}\\\\u_B = 6.366*10^6 \ J/m^3](https://tex.z-dn.net/?f=u%20_B%20%3D%20%5Cfrac%7BB%5E2%7D%7B2%5Cmu_o%7D%20%5C%5C%5C%5Cu%20_B%20%3D%20%5Cfrac%7B%284%29%5E2%7D%7B2%284%5Cpi%2A10%5E%7B-7%7D%29%7D%5C%5C%5C%5Cu_B%20%3D%206.366%2A10%5E6%20%5C%20J%2Fm%5E3)
(b) The energy stored in the magnetic field within the solenoid
![U_B = u_B V\\\\U_B = u_B AL](https://tex.z-dn.net/?f=U_B%20%3D%20u_B%20V%5C%5C%5C%5CU_B%20%3D%20u_B%20AL)
![U_B = u_B(A)(L)\\\\U_B = 6.366*10^6(\pi * 0.031^2)(0.26) \\\\U_B = 4997.69 J\\\\U_B = 5 \ KJ\\](https://tex.z-dn.net/?f=U_B%20%3D%20u_B%28A%29%28L%29%5C%5C%5C%5CU_B%20%3D%206.366%2A10%5E6%28%5Cpi%20%2A%200.031%5E2%29%280.26%29%20%5C%5C%5C%5CU_B%20%3D%204997.69%20J%5C%5C%5C%5CU_B%20%3D%205%20%5C%20KJ%5C%5C)
Hi there!
We can begin by solving for the linear acceleration as we are given sufficient values to do so.
We can use the following equation:
vf = vi + at
Plug in given values:
4 = 9.7 + 4.4a
Solve for a:
a = -1.295 m/s²
We can use the following equation to convert from linear to angular acceleration:
a = αr
a/r = α
Thus:
-1.295/0.61 = -2.124 rad/sec² ⇒ 2.124 rad/sec² since counterclockwise is positive.
Now, we can find the angular displacement using the following:
θ = ωit + 1/2αt²
We must convert the initial velocity of the tire (9.7 m/s) to angular velocity:
v = ωr
v/r = ω
9.7/0.61 = 15.9 rad/sec
Plug into the equation:
θ = 15.9(4.4) + 1/2(2.124)(4.4²) = 20.56 rad
if the pointy thingy in your compass is pointing north, that means it's being (pulled toward) something near Earth's north pole
Answer:
The wavelength of the emitted radiation is inversely proportional to its frequency, or λ = c/ν. The value of Planck's constant is defined as 6.62607015 × 10−34 joule∙second.
Explanation:
Planck's quantum theory. According to Planck's quantum theory, Different atoms and molecules can emit or absorb energy in discrete quantities only. The smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as quantum.
Hope this helps!