Answer:
v = 2.19 m/s Anti-clockwise
Explanation:
Given data:
L = 28.5 cm
magnetic field = 1.60 T
Induced emf 1.00 V
Induced emf[tex] = \frac{d\phi}{dt}[/tex]
[tex]\epsilon_{in} = \frac{d}{dt} BA[/tex]
Where A is area
area at any point A = Lx
[tex]\epsilon_{in} = \frac{d}{dt} BLx[/tex]
[tex]\epsilon_{in} = BL \frac{dx}{dt}[/tex]
[tex]\epsilon_{in} = BLv[tex]1 = 1.6\times 0.285 v[/tex]
v = 2.19 m/s
b) Induced emf & induced current are such that they oppose the change is flux.
As the area decreases with rod shift to left, hence the flux decreases. And induced emf will generate induced current in a such a way that induced magnetic field will be in direction of initial magnetic field. Therefore Anti-clockwise
a) The rod moves at a speed of 2.193 meters per second.
b) By Lenz's law the induced current is moving from the upper metal bar to the lower metal bar.
a) The Lenz's law states that induced electromotive force ([tex]\epsilon_{ind}[/tex]), in volts, is opposed to the change in magnetic flux ([tex]\phi_{B}[/tex]), in tesla-square meters, whose formula is:
[tex]\epsilon_{ind} = -\frac{d\phi_{B}}{dt}[/tex] (1)
Where the magnetic flux is defined by following formula:
[tex]\phi_{B} = B\cdot A\cdot \cos \theta[/tex] (2)
Where:
If we know that the magnetic field is parallel to the area vector, then we have the following reduction and we derive an expression for the conducting rod:
[tex]\phi_{B} = B\cdot A[/tex] (2b)
(2b) in (1):
[tex]\epsilon_{ind} = \frac{d}{dt} (\phi_{B})[/tex]
[tex]\epsilon_{ind} = \frac{dB}{dt}\cdot A + B\cdot \frac{dA}{dt}[/tex]
[tex]\epsilon_{ind} = B\cdot \frac{dA}{dt}[/tex]
[tex]\epsilon_{ind} = B\cdot l \cdot \frac{dx}{dt}[/tex] (3)
Where:
If we know that [tex]\epsilon_{ind} = 1\,V[/tex], [tex]B = 1.60\,T[/tex] and [tex]l = 0.285\,m[/tex], then the velocity of the conducting rod is:
[tex]\frac{dx}{dt} = \frac{\epsilon_{ind}}{B\cdot l}[/tex]
[tex]\frac{dx}{dt} = \frac{1\,V}{(1.60\,T)\cdot (0.285\,m)}[/tex]
[tex]\frac{dx}{dt} = 2.193\,\frac{m}{s}[/tex]
The rod moves at a speed of 2.193 meters per second to the right. [tex]\blacksquare[/tex]
b) Because of the Lenz's law, the magnetic flux is increasing inasmuch the conducting rod is moving to the right and the induced current is moving to the left, from the upper metal bar to the lower metal bar. [tex]\blacksquare[/tex]
To learn more on Lenz's law, we kindly invite to check this verified question: https://brainly.com/question/13744192
