a) 57.5 m/s
b) Yes
Explanation:
a)
According to Faraday-Newmann-Lenz's law, the electromotive force induced in the coil due to the change in magnetic flux through it is given by:
[tex]\epsilon=-\frac{N \Delta \Phi}{\Delta t}[/tex]
where
N is the number of turns in the coil
[tex]\Delta \Phi[/tex] is the change in magnetic flux
[tex]\Delta t[/tex] is the time interval
The change in magnetic flux can be written as
[tex]\Delta \Phi = A\Delta B[/tex]
where
A is the area of the coil
[tex]\Delta B[/tex] is the variation of the strength of the magnetic field
Re-writing the equation,
[tex]\epsilon=-\frac{NA\Delta B}{\Delta t}[/tex]
To make the bulb glowing, the induced emf must be:
[tex]\epsilon=1.5 V[/tex]
And we also have:
N = 100
[tex]\Delta B=0 T-3.6\cdot 10^{-2} T=-0.036 T[/tex]
[tex]A=2.9\cdot 10^{-4} m^2[/tex]
So we can find the maximum time required to induce this emf:
[tex]\Delta t=-\frac{NA\Delta B}{\epsilon}=-\frac{(100)(2.9\cdot 10^{-4})(-0.036)}{1.5}=6.96\cdot 10^{-4} s[/tex]
Since the length to cover in this time is
L = 4.0 cm = 0.04 m
The speed should be
[tex]v=\frac{L}{t}=\frac{0.04}{6.96\cdot 10^{-4}}=57.5 m/s[/tex]
b)
Yes: if the coil is moved at a speed of 57.7 m/s, then the potential difference induced in the bulb will be 1.5 V, which is enough to make the bulb glowing.
