A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad ${\mathrm{s}}^{-1}$   in a uniform horizontal magnetic field  ${\mathrm{3.0\times 10}}^{\mathrm{-2}}\mathrm{T}$  of .  The maximum emf induced the coil will be ________ ${\mathrm{\times 10}}^{\mathrm{2}}$ volt.

Given, radius of circular coil, r = 8.0 cm = 0.08 m

Number of turns, N = 20

Angular speed of coil, ω = 50 rad s^-1

Magnetic field, $\mathrm{B}=3.0\times {10}^{-2} \mathrm{T}$

The maximum emf induced in a coil can be expressed as

                   ε = ω NBA

Here, A is the area of coil.

                 ε = NB ω ( πr² )

Substituting the given values, we get

                  $\begin{array}{l}\mathrm{\epsilon }=20\times 3.0\times {10}^{-2}\times 50\times \mathrm{\pi }\times (0.08{)}^2\\ =60.3\times {10}^{-2}\mathrm{V}\\ \simeq 60\times {10}^{-2}\mathrm{V}\end{array}$