Question

In a physics laboratory experiment, a coil with 250 turns enclosing an area of 10.5 cm2 is rotated during the time interval 3.10×10−2 s from a position in which its plane is perpendicular to earth's magnetic field to one in which its plane is parallel to the field. the magnitude of earth's magnetic field at the lab location is 5.30×10−5 t .

Answer 1

I guess the problem is asking for the induced emf in the coil.

Faraday-Neumann-Lenz states that the induced emf in a coil is given by:
$\epsilon = -N \frac{\Delta \Phi}{\Delta t}$
where
N is the number of turns in the coil
$\Delta \Phi$ is the variation of magnetic flux through the coil
$\Delta t$ is the time interval

The coil is initially perpendicular to the Earth's magnetic field, so the initial flux through it is given by the product between the magnetic field strength and the area of the coil:
$\Phi_i = BA=(5.30 \cdot 10^{-5}T)(10.5 \cdot 10^{-4} m^2)=5.57 \cdot 10^{-8} Wb$
At the end of the time interval, the coil is parallel to the field, so the final flux is zero:
$\Phi_f = 0$

Therefore, we can calculate now the induced emf by using the first formula:
$\epsilon = -N \frac{\Delta \Phi}{\Delta t}=- (250) \frac{5.57 \cdot 10^{-8} Wb - 0}{3.10 \cdot 10^{-2} s} = -4.5 \cdot 10^{-4} V$