Expand each vector into their component forms:

Similarly,


Then assuming the resultant vector
is the sum of these three vectors, we have


and so
has magnitude

and direction
such that

Answer:
2.36 μ H
Explanation:
Given,
Number of turns= 90
diameter = 1.3 cm = 0.013 m
unscratched length = 57 cm = 0.57 m
Area, A = π r²
= π x 0.0065² = 1.32 x 10⁻⁴ m²
we know,


L = 2.36 μ H
Hence, the inductance of the unstretched cord is equal to 2.36 μ H
Answer:
Weight of the dog on surface of earth is 140.14 Newton.
Given:
mass of the dog = 14.3 kg
To find:
Weight of the dog = ?
Formula used:
Weight of the dog is given by,
W = mg
Where, W = weight of the dog
m = mass of the dog
g = acceleration due to gravity
Solution:
Weight of the dog is given by,
W = mg
Where, W = weight of the dog
m = mass of the dog = 14.3 kg
g = acceleration due to gravity
W = 14.3 × 9.8
W = 140.14 Newton
Weight of the dog on surface of earth is 140.14 Newton.
Answer:
FB = 0.187 N
Explanation:
To find the magnetic force FB in the wire you use the following formula:

the angle between B and L is given by:

Due to B depends on "y" you take into account the contribution of each element dy of the wire to the magnitude of the magnetic force. Thus, you have to integrate the following expression:
![|\vec{F_B}|=Isin\theta\int_0^{0.25}B(y)dy=Isin\theta\int_0^{0.25}(0.5y)dy\\\\|\vec{F_B}|=(2.0*10^{-3}A)(sin36.86\°)(0.5T)[\frac{0.25^2}{2}m]=0.187\ N](https://tex.z-dn.net/?f=%7C%5Cvec%7BF_B%7D%7C%3DIsin%5Ctheta%5Cint_0%5E%7B0.25%7DB%28y%29dy%3DIsin%5Ctheta%5Cint_0%5E%7B0.25%7D%280.5y%29dy%5C%5C%5C%5C%7C%5Cvec%7BF_B%7D%7C%3D%282.0%2A10%5E%7B-3%7DA%29%28sin36.86%5C%C2%B0%29%280.5T%29%5B%5Cfrac%7B0.25%5E2%7D%7B2%7Dm%5D%3D0.187%5C%20N)
hence, the magnitude of the magnetic force is 0.187N