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:
where
N is the number of turns in the coil
is the change in magnetic flux
is the time interval
The change in magnetic flux can be written as
where
A is the area of the coil
is the variation of the strength of the magnetic field
Re-writing the equation,
To make the bulb glowing, the induced emf must be:
And we also have:
N = 100
So we can find the maximum time required to induce this emf:
Since the length to cover in this time is
L = 4.0 cm = 0.04 m
The speed should be
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.