Answer: AAAAAAAAGGGGGHHHHJJJGSSSUUUUUUUUYCCFVGBHNJM
Explanation: YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET YEET
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.
Answer:
Option (2)
Explanation:
From the figure attached,
Horizontal component, ![A_x=A\text{Sin}37](https://tex.z-dn.net/?f=A_x%3DA%5Ctext%7BSin%7D37)
![A_x=12[\text{Sin}(37)]](https://tex.z-dn.net/?f=A_x%3D12%5B%5Ctext%7BSin%7D%2837%29%5D)
= 7.22 m
Vertical component, ![A_y=A[\text{Cos}(37)]](https://tex.z-dn.net/?f=A_y%3DA%5B%5Ctext%7BCos%7D%2837%29%5D)
= 9.58 m
Similarly, Horizontal component of vector C,
= C[Cos(60)]
= 6[Cos(60)]
= ![\frac{6}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B2%7D)
= 3 m
![C_y=6[\text{Sin}(60)]](https://tex.z-dn.net/?f=C_y%3D6%5B%5Ctext%7BSin%7D%2860%29%5D)
= 5.20 m
Resultant Horizontal component of the vectors A + C,
m
= 4.38 m
Now magnitude of the resultant will be,
From ΔOBC,
![R=\sqrt{(R_x)^{2}+(R_y)^2}](https://tex.z-dn.net/?f=R%3D%5Csqrt%7B%28R_x%29%5E%7B2%7D%2B%28R_y%29%5E2%7D)
= ![\sqrt{(4.22)^2+(4.38)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%284.22%29%5E2%2B%284.38%29%5E2%7D)
= ![\sqrt{17.81+19.18}](https://tex.z-dn.net/?f=%5Csqrt%7B17.81%2B19.18%7D)
= 6.1 m
Direction of the resultant will be towards vector A.
tan(∠COB) = ![\frac{\text{CB}}{\text{OB}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BCB%7D%7D%7B%5Ctext%7BOB%7D%7D)
= ![\frac{R_y}{R_x}](https://tex.z-dn.net/?f=%5Cfrac%7BR_y%7D%7BR_x%7D)
= ![\frac{4.38}{4.22}](https://tex.z-dn.net/?f=%5Cfrac%7B4.38%7D%7B4.22%7D)
m∠COB = ![\text{tan}^{-1}(1.04)](https://tex.z-dn.net/?f=%5Ctext%7Btan%7D%5E%7B-1%7D%281.04%29)
= 46°
Therefore, magnitude of the resultant vector will be 6.1 m and direction will be 46°.
Option (2) will be the answer.
Add all the resistances across the circuit together the calculate the total resistance