Given :
An electron moving in the positive x direction experiences a magnetic force in the positive z direction.
To Find :
The direction of the magnetic field.
Solution :
We know, force is given by :
![\vec{F}=q(\vec{v}\times \vec{B)}](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%3Dq%28%5Cvec%7Bv%7D%5Ctimes%20%5Cvec%7BB%29%7D)
Here, q = -e.
![\vec{F}=(-e)(\vec{v}\times \vec{B)}\\\\\hat{k}=(-e)(\hat{i}\times \vec{B})](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%3D%28-e%29%28%5Cvec%7Bv%7D%5Ctimes%20%5Cvec%7BB%29%7D%5C%5C%5C%5C%5Chat%7Bk%7D%3D%28-e%29%28%5Chat%7Bi%7D%5Ctimes%20%5Cvec%7BB%7D%29)
Now, for above condition to satisfy :
![\hat{i}\times \vec{B}=-\hat{k}](https://tex.z-dn.net/?f=%5Chat%7Bi%7D%5Ctimes%20%5Cvec%7BB%7D%3D-%5Chat%7Bk%7D)
So, ![\vec{B}=-\hat{j}](https://tex.z-dn.net/?f=%5Cvec%7BB%7D%3D-%5Chat%7Bj%7D)
Therefore, direction of magnetic field is negative y direction.
Hence, this is the required solution.
(1)
Cheetah speed: ![v_c = 97.8 km/h=27.2 m/s](https://tex.z-dn.net/?f=v_c%20%3D%2097.8%20km%2Fh%3D27.2%20m%2Fs)
Its position at time t is given by
(1)
Gazelle speed: ![v_g = 78.2 km/h=21.7 m/s](https://tex.z-dn.net/?f=v_g%20%3D%2078.2%20km%2Fh%3D21.7%20m%2Fs)
the gazelle starts S0=96.8 m ahead, therefore its position at time t is given by
(2)
The cheetah reaches the gazelle when
. Therefore, equalizing (1) and (2) and solving for t, we find the time the cheetah needs to catch the gazelle:
![v_c t=S_0 + v_g t](https://tex.z-dn.net/?f=v_c%20t%3DS_0%20%2B%20v_g%20t)
![(v_c -v_g t)=S_0](https://tex.z-dn.net/?f=%28v_c%20-v_g%20t%29%3DS_0)
![t=\frac{S_0}{v_c-v_t}=\frac{96.8 m}{27.2 m/s-21.7 m/s}=17.6 s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7BS_0%7D%7Bv_c-v_t%7D%3D%5Cfrac%7B96.8%20m%7D%7B27.2%20m%2Fs-21.7%20m%2Fs%7D%3D17.6%20s)
(2) To solve the problem, we have to calculate the distance that the two animals can cover in t=7.5 s.
Cheetah: ![S_c = v_c t =(27.2 m/s)(7.5 s)=204 m](https://tex.z-dn.net/?f=S_c%20%3D%20v_c%20t%20%3D%2827.2%20m%2Fs%29%287.5%20s%29%3D204%20m)
Gazelle: ![S_g = v_g t =(21.7 m/s)(7.5 s)=162.8 m](https://tex.z-dn.net/?f=S_g%20%3D%20v_g%20t%20%3D%2821.7%20m%2Fs%29%287.5%20s%29%3D162.8%20m)
So, the gazelle should be ahead of the cheetah of at least
![d=S_c -S_g =204 m-162.8 m=41.2 m](https://tex.z-dn.net/?f=d%3DS_c%20-S_g%20%3D204%20m-162.8%20m%3D41.2%20m)
Answer:
Invisible UV energy reacts with emulsion sensitizer and hardens the stencil so it won't dissolve with water and rinse down the drain
Explanation:
Answer:
solar, wind, hydro, natural resources