Answer:
The magnitude of magnetic field at given point =
×
T
Explanation:
Given :
Current passing through both wires = 5.0 A
Separation between both wires = 8.0 cm
We have to find magnetic field at a point which is 5 cm from any of wires.
From biot savert law,
We know the magnetic field due to long parallel wires.
⇒ ![B = \frac{\mu_{0}i }{2\pi R}](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B%5Cmu_%7B0%7Di%20%7D%7B2%5Cpi%20R%7D)
Where
magnetic field due to long wires,
,
perpendicular distance from wire to given point
From any one wire
5 cm,
3 cm
so we write,
∴ ![B = B_{1} + B_{2}](https://tex.z-dn.net/?f=B%20%3D%20B_%7B1%7D%20%2B%20B_%7B2%7D)
![B = \frac{\mu_{0} i}{2\pi R_{1} } + \frac{\mu_{0} i}{2\pi R_{2} }](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B%5Cmu_%7B0%7D%20i%7D%7B2%5Cpi%20R_%7B1%7D%20%7D%20%2B%20%20%5Cfrac%7B%5Cmu_%7B0%7D%20i%7D%7B2%5Cpi%20R_%7B2%7D%20%7D)
![B =\frac{ 4\pi \times10^{-7} \times5}{2\pi } [\frac{1}{0.03} + \frac{1}{0.05} ]](https://tex.z-dn.net/?f=B%20%3D%5Cfrac%7B%204%5Cpi%20%5Ctimes10%5E%7B-7%7D%20%5Ctimes5%7D%7B2%5Cpi%20%7D%20%5B%5Cfrac%7B1%7D%7B0.03%7D%20%2B%20%5Cfrac%7B1%7D%7B0.05%7D%20%5D)
![B = 5.33\times10^{-5} T](https://tex.z-dn.net/?f=B%20%3D%205.33%5Ctimes10%5E%7B-5%7D%20%20T)
Therefore, the magnitude of magnetic field at given point = ![5.33\times10^{-5} T](https://tex.z-dn.net/?f=5.33%5Ctimes10%5E%7B-5%7D%20T)
Answer:
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Answer:
The correct answer is B
Explanation:
Let's calculate the electric field using Gauss's law, which states that the electric field flow is equal to the charge faced by the dielectric permittivity
Φ
= ∫ E. dA =
/ ε₀
For this case we create a Gaussian surface that is a sphere. We can see that the two of the sphere and the field lines from the spherical shell grant in the direction whereby the scalar product is reduced to the ordinary product
∫ E dA =
/ ε₀
The area of a sphere is
A = 4π r²
E 4π r² =
/ ε₀
E = (1 /4πε₀
) q / r²
Having the solution of the problem let's analyze the points:
A ) r = 3R / 4 = 0.75 R.
In this case there is no charge inside the Gaussian surface therefore the electric field is zero
E = 0
B) r = 5R / 4 = 1.25R
In this case the entire charge is inside the Gaussian surface, the field is
E = (1 /4πε₀
) Q / (1.25R)²
E = (1 /4πε₀
) Q / R2 1 / 1.56²
E₀ = (1 /4π ε₀
) Q / R²
= Eo /1.56
²
= 0.41 Eo
C) r = 2R
All charge inside is inside the Gaussian surface
=(1 /4π ε₀
) Q 1/(2R)²
= (1 /4π ε₀
) q/R² 1/4
= Eo 1/4
= 0.25 Eo
D) False the field changes with distance
The correct answer is B
Answer:
about 602 milliseconds
Explanation:
The motion can be approximated by the equation ...
y = -4.9t^2 -22.8t +15.5
where t is the time since the arrow was released, and y is the distance above the ground.
When y=0, the arrow has hit the ground.
Using the quadratic formula, we find ...
t = (-(-22.8) ± √((-22.8)^2 -4(-4.9)(15.5)))/(2(-4.9))
= (22.8 ± √823.64)/(-9.8)
The positive solution is ...
t ≈ 0.60195193
It takes about 602 milliseconds for the arrow to reach the ground.
<h2>
Option A is the correct answer.</h2>
Explanation:
Acceleration due to gravity
![g=\frac{GM}{r^2}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7BGM%7D%7Br%5E2%7D)
G = 6.67 × 10⁻¹¹ m² kg⁻¹ s⁻²
Let mass of earth be M and radius of earth be r.
We have
![g=\frac{GM}{r^2}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7BGM%7D%7Br%5E2%7D)
Now
A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.
Mass of hypothetical planet, M' = M/2
Radius of hypothetical planet, r' = 2r
Substituting
![g'=\frac{GM'}{r'^2}\\\\g'=\frac{G\times \frac{M}{2}}{(2r)^2}\\\\g'=\frac{\frac{GM}{r^2}}{8}\\\\g'=\frac{g}{8}](https://tex.z-dn.net/?f=g%27%3D%5Cfrac%7BGM%27%7D%7Br%27%5E2%7D%5C%5C%5C%5Cg%27%3D%5Cfrac%7BG%5Ctimes%20%5Cfrac%7BM%7D%7B2%7D%7D%7B%282r%29%5E2%7D%5C%5C%5C%5Cg%27%3D%5Cfrac%7B%5Cfrac%7BGM%7D%7Br%5E2%7D%7D%7B8%7D%5C%5C%5C%5Cg%27%3D%5Cfrac%7Bg%7D%7B8%7D)
Option A is the correct answer.