the answer should be:
When the buoyant force is equal to the force of gravity
Answer:
Magnesium atomic no. = 24,25,26. These are the two elements which have same atomic no
Explanation:
<em>Another key factor that determines a star's colour is its temperature. As stars become hotter, the overall radiated energy increases, and the peak of the curve changes to shorter wavelengths. To put it another way, when a star heats up, the light it produces moves toward the blue end of the spectrum.</em>
To solve this problem it is necessary to apply the concepts related to the Force since Newton's second law, as well as the concept of Electromagnetic Force. The relationship of the two equations will allow us to find the magnetic field through the geometric relations of density and volume.
![F_{mag}= BIL](https://tex.z-dn.net/?f=F_%7Bmag%7D%3D%20BIL)
Where,
B = Magnetic Field
I = Current
L = Length
<em>Note:
is a direct adaptation of the vector relation
</em>
From Newton's second law we know that the relation of Strength and weight is determined as
![F_g = mg](https://tex.z-dn.net/?f=F_g%20%3D%20mg)
Where,
m = Mass
g = Gravitational Acceleration
For there to be balance the two forces must be equal therefore
![F_{mag} = F_g](https://tex.z-dn.net/?f=F_%7Bmag%7D%20%3D%20F_g)
Our values are given as,
Diameter ![(d) = 1.0mm = 1*10^{-3}m](https://tex.z-dn.net/?f=%28d%29%20%3D%201.0mm%20%3D%201%2A10%5E%7B-3%7Dm)
Radius ![(r) = \frac{d}{2} = \frac{1*10^{-3}}{2} = 0.5*10^{-3}m](https://tex.z-dn.net/?f=%28r%29%20%3D%20%5Cfrac%7Bd%7D%7B2%7D%20%3D%20%5Cfrac%7B1%2A10%5E%7B-3%7D%7D%7B2%7D%20%3D%200.5%2A10%5E%7B-3%7Dm)
Magnetic Field ![(B) = 5.0*10^{-5} T](https://tex.z-dn.net/?f=%28B%29%20%3D%205.0%2A10%5E%7B-5%7D%20T)
From the relationship of density another way of expressing mass would be
![\rho = \frac{m}{V} \rightarrow m = \rho V](https://tex.z-dn.net/?f=%5Crho%20%3D%20%5Cfrac%7Bm%7D%7BV%7D%20%5Crightarrow%20m%20%3D%20%5Crho%20V)
At the same time the volume ratio for a cylinder (the shape of the wire) would be
![V = \pi r^2 L \rightarrow L =Length, r= Radius](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2%20L%20%5Crightarrow%20L%20%3DLength%2C%20r%3D%20Radius)
Replacing this two expression at our first equation we have that:
![BIL = mg](https://tex.z-dn.net/?f=BIL%20%3D%20mg)
![BIL = ( \rho V)g](https://tex.z-dn.net/?f=BIL%20%3D%20%28%20%5Crho%20V%29g)
![BIL = ( \rho \pi r^2 L)g](https://tex.z-dn.net/?f=BIL%20%3D%20%28%20%5Crho%20%5Cpi%20r%5E2%20L%29g)
Re-arrange to find I
![I = \frac{( \rho \pi r^2 L)g}{BL}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B%28%20%5Crho%20%5Cpi%20r%5E2%20L%29g%7D%7BBL%7D)
![I = \frac{( \rho \pi r^2 )g}{B}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B%28%20%5Crho%20%5Cpi%20r%5E2%20%29g%7D%7BB%7D)
We have for definition that the Density of copper is
, gravity acceleration is
and the values of magnetic field (B) and the radius were previously given, then:
![I = \frac{( (8.9*10^3 ) \pi (0.5*10^{-3})^2 )(9.8)}{5.0*10^{-5}}](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B%28%20%288.9%2A10%5E3%20%29%20%5Cpi%20%280.5%2A10%5E%7B-3%7D%29%5E2%20%29%289.8%29%7D%7B5.0%2A10%5E%7B-5%7D%7D)
![I = 1370.05A](https://tex.z-dn.net/?f=I%20%3D%201370.05A)
The current is too high to be transported which would make the case not feasible.
Answer:
(C). The line integral of the magnetic field around a closed loop
Explanation:
Faraday's law states that induced emf is directly proportional to the time rate of change of magnetic flux.
This can be written mathematically as;
![EMF = -\frac{\delta \phi _B}{\delta t}](https://tex.z-dn.net/?f=EMF%20%3D%20-%5Cfrac%7B%5Cdelta%20%5Cphi%20_B%7D%7B%5Cdelta%20t%7D)
is the rate of change of the magnetic flux through a surface bounded by the loop.
ΔФ = BA
where;
ΔФ is change in flux
B is the magnetic field
A is the area of the loop
Thus, according to Faraday's law of electric generators
∫BdL =
= EMF
Therefore, the line integral of the magnetic field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop.
The correct option is "C"
(C). The line integral of the magnetic field around a closed loop