David Sang and Graham Jones Solutions for Chapter: Electromagnetic Induction, Exercise 5: Questions

$A$ conductor of length $L$ moves at a steady speed $v$ at right angles to a uniform magnetic field of flux density $B$.  

Show that the magnitude of the induced $e.m.f. E$ across the ends of the conductor is given by the equation$: e=BLv$.

A wire of length $10 cm$ is moved through a distance  of$2.0 cm$ in a direction at right angles to its length in the space between the poles of a magnet, and perpendicular to the magnetic field . The flux density is $1.5 T$ If this takes $0.50 s,$, calculate the magnitude of the average induced e.m.f. across th ends of the wire.

Figure, shows a search coil with$2000$ turns and cross-sectional area $1.2 c{m}^2$. It is placed between the poles of a strong magnet. The magnetic field is perpendicular to the plane of the coil. The ends of the coil are connected to a voltmeter. The coil is then pulled out of the magnetic field, and the voltmeter records an average induced e.m.f. of$0.40V$ over a time interval of $0.20s.$
Calculate the magnetic flux density between the
poles of the magnet.

Using a search coil to determine the magnetic flux density of the field between the poles of this magnet.