Answer:
18.6012339739 A
Explanation:
= Vacuum permeability = ![4\pi \times 10^{-7}\ H/m](https://tex.z-dn.net/?f=4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5C%20H%2Fm)
L = Length of wire = 55 cm
N = Number of turns = 4000
I = Current
Magnetic field is given by
![B=\dfrac{\mu_0NI}{L}\\\Rightarrow I=\dfrac{BL}{\mu_0N}\\\Rightarrow I=\dfrac{0.17\times 0.55}{4\pi \times 10^{-7}\times 4000}\\\Rightarrow I=18.6012339739\ A](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Cmu_0NI%7D%7BL%7D%5C%5C%5CRightarrow%20I%3D%5Cdfrac%7BBL%7D%7B%5Cmu_0N%7D%5C%5C%5CRightarrow%20I%3D%5Cdfrac%7B0.17%5Ctimes%200.55%7D%7B4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%204000%7D%5C%5C%5CRightarrow%20I%3D18.6012339739%5C%20A)
The current necessary to produce this field is 18.6012339739 A
The H field is in units of amps/meter. It is sometimes called the auxiliary field. It describes the strength (or intensity) of a magnetic field. The B field is the magnetic flux density. It tells us how dense the field is. If you think about a magnetic field as a collection of magnetic field lines, the B field tells us how closely they are spaced together. These lines (flux linkages) are measured in a unit called a Weber (Wb). This is the analog to the electric charge, the Coulomb. Just like electric flux density (the D field, given by D=εE) is Coulombs/m², The B field is given by Wb/m², or Tesla. The B field is defined to be μH, in a similar way the D field is defined. Thus B is material dependent. If you expose a piece of iron (large μ) to an H field, the magnetic moments (atoms) inside will align in the field and amplify it. This is why we use iron cores in electromagnets and transformers.
So if you need to measure how much flux goes through a loop, you need the flux density times the area of the loop Φ=BA. The units work out like
Φ=[Wb/m²][m²]=[Wb], which is really just the amount of flux. The H field alone can't tell you this because without μ, we don't know the "number of field" lines that were caused in the material (even in vacuum) by that H field. And the flux cares about the number of lines, not the field intensity.
I'm way into magnetic fields, my PhD research is in this area so I could go on forever. I have included a picture that also shows M, the magnetization of a material along with H and B. M is like the polarization vector, P, of dielectric materials. If you need more info let me know but I'll leave you alone for now!
the electric force decreases because the distance has an indirect relationship to the force
Explanation:
The electric force between two objects is given by
![F=k \frac{q_1 q_2}{r^2}](https://tex.z-dn.net/?f=F%3Dk%20%5Cfrac%7Bq_1%20q_2%7D%7Br%5E2%7D)
where
k is the Coulomb's constant
q1 and q2 are the charges of the two objects
r is the distance between the two objects
As we can see from the formula, the magnitude of the force is inversely proportional to the square of the distance: so, when the distance between the object increases, the magnitude of the force decreases.
Hi there!
![\large\boxed{\text{B) 20 meters}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7BB%29%2020%20meters%7D%7D)
We know that:
![E_T = U + K](https://tex.z-dn.net/?f=E_T%20%3D%20U%20%2B%20K)
U = Potential Energy (J)
K = Kinetic Energy (J)
E = Total Energy (J)
At 10m, the total amount of energy is equivalent to:
U + K = 50 + 50 = 100 J
To find the highest point the object can travel, K = 0 J and U is at a maximum of 100 J, so:
100J = mgh
We know at 10m U = 50J, so we can solve for mass. Let g = 10 m/s².
50J = 10(10)m
m = 1/2 kg
Now, solve for height given that E = 100 J:
100J = 1/2(10)h
100J = 5h
<u>h = 20 meters</u>
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