Answer to Question #133745 in Electricity and Magnetism for Ranu

Question

A closed circular coil having a diameter of 50 cm made of 200 turns of wire with a total resistance of 10 Ω is placed with its plane at right angles to a magnetic field of strength of 10-2 T. Calculate the quantity of electric charge passing through it when the coil is turned through 1800 about an axis in its plane. 

Answer 1

We know that electromotive force is

$\displaystyle \mathcal {E} = - \frac{\Delta \Phi}{\Delta t}$

$\Phi = NBS$ - a flux though the coil

$\Delta \Phi = \Phi (cos{180^\circ} - cos{0^\circ})= -2 \Phi$

By definition, current is

$\displaystyle I = \frac{\Delta q}{\Delta t}$

and according to the Ohm's law $\displaystyle I = \frac{\mathcal{E}}{R}$

Combining all these formulae, we have

$\displaystyle \Delta q = \frac{2 \Phi}{R} = \frac{2 NBS}{R} = \frac{2 \cdot200 \cdot 10^{-2} \cdot (\pi \cdot 0.5^2/4)}{10} = 7.85 \cdot 10^{-2} C$