The <span>induced emf in the coil is -45V.</span>
A concave lens is a lens that has at least one of its surfaces or both surfaces curved inwards. Due to this reason, this lens diverges the light that falls on it and hence is also called a diverging lens. The concave lens is thinner in the middle compared to its edges. These are used in flashlights, binoculars, telescopes, etc.
Please see attached image for reference.
To make sure that we have enough resourses to sustain ourselves. You see, if we use up, say, all water on earth, then obviously we won't have any more and we'll die.
Answer:
a).β=0.53
T
a).β=0.40
T
Explanation:
The magnetic field at distance 'r' from the center of toroid is given by:
![\beta =\frac{u_{o}*I*N}{2\pi*r}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%5Cfrac%7Bu_%7Bo%7D%2AI%2AN%7D%7B2%5Cpi%2Ar%7D)
a).
![N=500\\I=0.800A\\r=15cm*\frac{1m}{100cm}=0.15m\\u_{o}=4\pi x10^{-7}\frac{T*m}{A} \\\beta=\frac{4\pi x10^{-7}\frac{T*m}{A}*0.8A*500}{2\pi*0.15m} \\\beta=0.53x10^{-3}T](https://tex.z-dn.net/?f=N%3D500%5C%5CI%3D0.800A%5C%5Cr%3D15cm%2A%5Cfrac%7B1m%7D%7B100cm%7D%3D0.15m%5C%5Cu_%7Bo%7D%3D4%5Cpi%20x10%5E%7B-7%7D%5Cfrac%7BT%2Am%7D%7BA%7D%20%20%5C%5C%5Cbeta%3D%5Cfrac%7B4%5Cpi%20x10%5E%7B-7%7D%5Cfrac%7BT%2Am%7D%7BA%7D%2A0.8A%2A500%7D%7B2%5Cpi%2A0.15m%7D%20%5C%5C%5Cbeta%3D0.53x10%5E%7B-3%7DT)
b).
The distance is the radius add the cross section so:
![r_{1}=15cm+5cm\\r_{1}=20cm](https://tex.z-dn.net/?f=r_%7B1%7D%3D15cm%2B5cm%5C%5Cr_%7B1%7D%3D20cm)
![r_{1} =20cm*\frac{1m}{100cm}=0.20m](https://tex.z-dn.net/?f=r_%7B1%7D%20%3D20cm%2A%5Cfrac%7B1m%7D%7B100cm%7D%3D0.20m)
![\beta =\frac{u_{o}*I*N}{2\pi*r1}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%5Cfrac%7Bu_%7Bo%7D%2AI%2AN%7D%7B2%5Cpi%2Ar1%7D)
![\beta =\frac{4\pi x10^{-7}*0.80A*500 }{2\pi*0.20m} \\\beta=0.4x10^{-3} T](https://tex.z-dn.net/?f=%5Cbeta%20%3D%5Cfrac%7B4%5Cpi%20x10%5E%7B-7%7D%2A0.80A%2A500%20%7D%7B2%5Cpi%2A0.20m%7D%20%5C%5C%5Cbeta%3D0.4x10%5E%7B-3%7D%20T)
Answer:
Part a)
![v = 7.57 km/h](https://tex.z-dn.net/?f=v%20%3D%207.57%20km%2Fh)
Part b)
North of East
Explanation:
Speed of train towards East = 60 km/h
displacement towards East is given as
![d_1 = 40 km](https://tex.z-dn.net/?f=d_1%20%3D%2040%20km)
now it turns towards 50 degree East of North
so its distance is given as
![d_2 = 20 km(sin50 \hat i + cos50\hat j)](https://tex.z-dn.net/?f=d_2%20%3D%2020%20km%28sin50%20%5Chat%20i%20%2B%20cos50%5Chat%20j%29)
![d_2 = 15.3 \hat i + 12.8 \hat j](https://tex.z-dn.net/?f=d_2%20%3D%2015.3%20%5Chat%20i%20%2B%2012.8%20%5Chat%20j)
then finally it moves towards west for 50 min
![d_3 = -50 \hat i](https://tex.z-dn.net/?f=d_3%20%3D%20-50%20%5Chat%20i)
Now the total displacement of the train is given as
![d = d_1 + d_2 + d_3](https://tex.z-dn.net/?f=d%20%3D%20d_1%20%2B%20d_2%20%2B%20d_3)
![d = (40 + 15.3 - 50)\hat i + 12.8 \hat j](https://tex.z-dn.net/?f=d%20%3D%20%2840%20%2B%2015.3%20-%2050%29%5Chat%20i%20%2B%2012.8%20%5Chat%20j)
![d = 5.3\hat i + 12.8 \hat j](https://tex.z-dn.net/?f=d%20%3D%205.3%5Chat%20i%20%2B%2012.8%20%5Chat%20j)
now total time duration of the motion is given as
![T = 40 min + 20 min + 50 min](https://tex.z-dn.net/?f=T%20%3D%2040%20min%20%2B%2020%20min%20%2B%2050%20min%20)
![T = 1.83 h](https://tex.z-dn.net/?f=T%20%3D%201.83%20h)
now average velocity is given as
![v_{avg} = \frac{5.3\hat i + 12.8\hat j}{1.83}](https://tex.z-dn.net/?f=v_%7Bavg%7D%20%3D%20%5Cfrac%7B5.3%5Chat%20i%20%2B%2012.8%5Chat%20j%7D%7B1.83%7D)
![v_{avg} = 2.89\hat i + 6.99\hat j](https://tex.z-dn.net/?f=v_%7Bavg%7D%20%3D%202.89%5Chat%20i%20%2B%206.99%5Chat%20j)
Part a)
magnitude of the average velocity is given as
![v = \sqrt{v_x^2 + v_y^2}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7Bv_x%5E2%20%2B%20v_y%5E2%7D)
![v = \sqrt{2.89^2 + 6.99^2}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B2.89%5E2%20%2B%206.99%5E2%7D)
![v = 7.57 km/h](https://tex.z-dn.net/?f=v%20%3D%207.57%20km%2Fh)
Part b)
Direction of the velocity is given as
![tan\theta = \frac{v_y}{v_x}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7Bv_y%7D%7Bv_x%7D)
![tan\theta = \frac{6.99}{2.89}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7B6.99%7D%7B2.89%7D)
North of East