A rectangular coil of 2500 turns and dimensions 80 cm × 50 cm is...

Since the coil is rotated about its vertical axis of symmetry, its area vector always lies in the horizontal plane. Therefore, the vertical component of the earth's magnetic field ($B_V$) is always parallel to the plane of the coil and does not contribute to the magnetic flux. Only the horizontal component ($B_H$) contributes to the changing magnetic flux.

The maximum induced EMF in the coil is given by:
$E_{\text{max}} = N A B_H \omega$

Given values:
$N = 2500$
$A = 80\text{ cm} \times 50\text{ cm} = 0.8\text{ m} \times 0.5\text{ m} = 0.4\text{ m}^2$
$B_H = 3 \times 10^{-5}\text{ T}$
$\omega = 200\text{ rad s}^{-1}$

Substituting the values into the formula:
$E_{\text{max}} = 2500 \times 0.4 \times 3 \times 10^{-5} \times 200$
$E_{\text{max}} = 1000 \times 6000 \times 10^{-5} = 6\text{ V}$

The maximum induced current in the coil is:
$I_{\text{max}} = \dfrac{E_{\text{max}}}{R}$

Given the resistance $R = 2\text{ }\Omega$:
$I_{\text{max}} = \dfrac{6}{2} = 3\text{ A}$

Answer: $3\text{ A}$