An imbalance between electrical charges
Gradually slow down to a safe speed well before entering the curve.
(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>
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(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>
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(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:
Moving a magnet might cause a change in the magnetic field going through the solenoid. Whether or not it will change depends on the movement.
According to Faraday's law of induction a voltage is induced in a coil by a change in the magnetic flux. Magnetic flux is defined as the dot product of the magnetic field (a vector field) by the area enclosed by a loop of the coil.
The voltage is induced by the variation of the magnetic flux:
Where
ε: electromotive fore
N: number of turns in the coil
ΦB: magnetic flux
Moving the magnet faster would increase the rare of change of the magnetic flux, resulting in higher induced voltage.
Turning the magnet upside down would invert the direction of the magnetic field, reversing the voltage induced.
Magnetic domain structure is responsible for the magnetic behavior of ferromagnetic materials like iron, nickel, cobalt and their alloys, and ferrimagnetic materials like ferrite. ... Magnetic domains form in materials which have magnetic ordering; that is, their dipoles spontaneously align due to the exchange interaction.
