Answer:
The change in length per unit length per degree rise in temperature of copper is 0.000017k
Explanation:
Given that :
The linear expansivity of copper is 0.000017k. This simply means that ; for a given copper length, the length of such copper will increase by 0.000017k for every degree rose in temperature of the copper rod.
Therefore, the change in length per unit length per degree rise in temperature (k) is 0.000017
Answer:8 meters
Explanation:100cm is a meter
Answer:
The magnetic field along x axis is
![B_{x}=1.670\times10^{-10}\ T](https://tex.z-dn.net/?f=B_%7Bx%7D%3D1.670%5Ctimes10%5E%7B-10%7D%5C%20T)
The magnetic field along y axis is zero.
The magnetic field along z axis is
![B_{z}=3.484\times10^{-10}\ T](https://tex.z-dn.net/?f=B_%7Bz%7D%3D3.484%5Ctimes10%5E%7B-10%7D%5C%20T)
Explanation:
Given that,
Length of the current element ![dl=(0.5\times10^{-3})j](https://tex.z-dn.net/?f=dl%3D%280.5%5Ctimes10%5E%7B-3%7D%29j)
Current in y direction = 5.40 A
Point P located at ![\vec{r}=(-0.730)i+(0.390)k](https://tex.z-dn.net/?f=%5Cvec%7Br%7D%3D%28-0.730%29i%2B%280.390%29k)
The distance is
![|\vec{r}|=\sqrt{(0.730)^2+(0.390)^2}](https://tex.z-dn.net/?f=%7C%5Cvec%7Br%7D%7C%3D%5Csqrt%7B%280.730%29%5E2%2B%280.390%29%5E2%7D)
![|\vec{r}|=0.827\ m](https://tex.z-dn.net/?f=%7C%5Cvec%7Br%7D%7C%3D0.827%5C%20m)
We need to calculate the magnetic field
Using Biot-savart law
![B=\dfrac{\mu_{0}}{4\pi}\timesI\times\dfrac{\vec{dl}\times\vec{r}}{|\vec{r}|^3}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B%5Cmu_%7B0%7D%7D%7B4%5Cpi%7D%5CtimesI%5Ctimes%5Cdfrac%7B%5Cvec%7Bdl%7D%5Ctimes%5Cvec%7Br%7D%7D%7B%7C%5Cvec%7Br%7D%7C%5E3%7D)
Put the value into the formula
![B=10^{-7}\times5.40\times\dfrac{(0.5\times10^{-3})\times(-0.730)i+(0.390)k}{(0.827)^3}](https://tex.z-dn.net/?f=B%3D10%5E%7B-7%7D%5Ctimes5.40%5Ctimes%5Cdfrac%7B%280.5%5Ctimes10%5E%7B-3%7D%29%5Ctimes%28-0.730%29i%2B%280.390%29k%7D%7B%280.827%29%5E3%7D)
We need to calculate the value of ![\vec{dl}\times\vec{r}](https://tex.z-dn.net/?f=%5Cvec%7Bdl%7D%5Ctimes%5Cvec%7Br%7D)
![\vec{dl}\times\vec{r}=(0.5\times10^{-3})\times(-0.730)i+(0.390)k](https://tex.z-dn.net/?f=%5Cvec%7Bdl%7D%5Ctimes%5Cvec%7Br%7D%3D%280.5%5Ctimes10%5E%7B-3%7D%29%5Ctimes%28-0.730%29i%2B%280.390%29k)
![\vec{dl}\times\vec{r}=i(0.350\times0.5\times10^{-3}-0)+k(0+0.730\times0.5\times10^{-3})](https://tex.z-dn.net/?f=%5Cvec%7Bdl%7D%5Ctimes%5Cvec%7Br%7D%3Di%280.350%5Ctimes0.5%5Ctimes10%5E%7B-3%7D-0%29%2Bk%280%2B0.730%5Ctimes0.5%5Ctimes10%5E%7B-3%7D%29)
![\vec{dl}\times\vec{r}=0.000175i+0.000365k](https://tex.z-dn.net/?f=%5Cvec%7Bdl%7D%5Ctimes%5Cvec%7Br%7D%3D0.000175i%2B0.000365k)
Put the value into the formula of magnetic field
![B=10^{-7}\times5.40\times\dfrac{(0.000175i+0.000365k)}{(0.827)^3}](https://tex.z-dn.net/?f=B%3D10%5E%7B-7%7D%5Ctimes5.40%5Ctimes%5Cdfrac%7B%280.000175i%2B0.000365k%29%7D%7B%280.827%29%5E3%7D)
![B=1.670\times10^{-10}i+3.484\times10^{-10}k](https://tex.z-dn.net/?f=B%3D1.670%5Ctimes10%5E%7B-10%7Di%2B3.484%5Ctimes10%5E%7B-10%7Dk)
Hence, The magnetic field along x axis is
![B_{x}=1.670\times10^{-10}\ T](https://tex.z-dn.net/?f=B_%7Bx%7D%3D1.670%5Ctimes10%5E%7B-10%7D%5C%20T)
The magnetic field along y axis is zero.
The magnetic field along z axis is
![B_{z}=3.484\times10^{-10}\ T](https://tex.z-dn.net/?f=B_%7Bz%7D%3D3.484%5Ctimes10%5E%7B-10%7D%5C%20T)
Explanation:
Since the balloon is not accelerating means that the net force on the balloon is zero. This implies that the weight of balloon must be equal to the buoyant force on balloon.
Hence, the buoyant force equals the weight of air displaced by the balloon, also 20,000 N.
Weight of the air displaced = density of air × volume
The density of air at 1 atm pressure and 20º C is 1.2 kg/m³
the volume V = 20,000/(1.2×9.8) = 1700 m³
A Porsche will always win no matter what