(a) Differentiate the position vector to get the velocity vector:
<em>r</em><em>(t)</em> = (3.00 m/s) <em>t</em> <em>i</em> - (4.00 m/s²) <em>t</em>² <em>j</em> + (2.00 m) <em>k</em>
<em>v</em><em>(t)</em> = d<em>r</em>/d<em>t</em> = (3.00 m/s) <em>i</em> - (8.00 m/s²) <em>t</em> <em>j</em>
<em></em>
(b) The velocity at <em>t</em> = 2.00 s is
<em>v</em> (2.00 s) = (3.00 m/s) <em>i</em> - (16.0 m/s) <em>j</em>
<em></em>
(c) Compute the electron's position at <em>t</em> = 2.00 s:
<em>r</em> (2.00 s) = (6.00 m) <em>i</em> - (16.0 m) <em>j</em> + (2.00 m) <em>k</em>
The electron's distance from the origin at <em>t</em> = 2.00 is the magnitude of this vector:
||<em>r</em> (2.00 s)|| = √((6.00 m)² + (-16.0 m)² + (2.00 m)²) = 2 √74 m ≈ 17.2 m
(d) In the <em>x</em>-<em>y</em> plane, the velocity vector at <em>t</em> = 2.00 s makes an angle <em>θ</em> with the positive <em>x</em>-axis such that
tan(<em>θ</em>) = (-16.0 m/s) / (3.00 m/s) ==> <em>θ</em> ≈ -79.4º
or an angle of about 360º + <em>θ</em> ≈ 281º in the counter-clockwise direction.
Answer:
Explanation:
Electric field due to a charge Q at a point d distance away is given by the expression
E = k Q / d , k is a constant equal to 9 x 10⁹
Field due to charge = 3 X 10⁻⁹ C
E = E = 
Field due to charge = 4 X 10⁻⁹ C
![E = [tex]\frac{9\times 10^9\times4\times10^{-9}}{(2-d)^2}](https://tex.z-dn.net/?f=E%20%3D%20%5Btex%5D%5Cfrac%7B9%5Ctimes%2010%5E9%5Ctimes4%5Ctimes10%5E%7B-9%7D%7D%7B%282-d%29%5E2%7D)
These two fields will be equal and opposite to make net field zero
=
[/tex]


d = 0.928
The number converted is 
Explanation:
In order to convert from the original units to the final units, we have to keep in mind the following conversion factors:



The original unit that we have is

Therefore, it can be rewritten as:

Therefore, since the initial number was 0.779, the final value is

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Answer:
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Answer:
55407
Explanation:
we have given that magnetic field B=3.5 T
current through the coil=90 A
Length of solenoid =0.72 m
we know the formula of magnetic field

so 
so the number of turn in solenoid will be 55407