A circular coil of $$1000$$ turns each with area $$1$$ m$$^2$$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $$0.07$$ T. The maximum voltage generation will be ______ V.

A circular coil of $$1000$$ turns, each with area $$1$$ m$$^2$$, is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $$0.07$$ T. We need to find the maximum voltage generated.

Recall that the instantaneous EMF induced in a rotating coil is given by

$$\varepsilon = NBA\omega \sin(\omega t)$$

Since the maximum value occurs when $$\sin(\omega t) = 1$$, this leads to

$$\varepsilon_{max} = NBA\omega$$

As the coil completes one revolution per second, its angular frequency is

$$\omega = 2\pi f = 2\pi \times 1 = 2\pi \text{ rad/s}$$

Substituting $$N = 1000$$, $$B = 0.07$$ T, $$A = 1$$ m$$^2$$ and $$\omega = 2\pi$$ rad/s into the expression for $$\varepsilon_{max}$$ gives

$$\varepsilon_{max} = 1000 \times 0.07 \times 1 \times 2\pi$$

$$\varepsilon_{max} = 70 \times 2\pi = 140\pi$$

Evaluating this numerically yields

$$\varepsilon_{max} = 140 \times \frac{22}{7} = 140 \times 3.1429 = 440 \text{ V}$$

Therefore, the maximum voltage generated is 440 V.