Question

A flip coil consists of $N$ turns of circular coils which lie in a uniform magnetic field. Plane of the coils is perpendicular to the magnetic field as shown in figure. The coil is connected to a current integrator which measures the total charge passing through it. The coil is turned through ${180}^o$ about the diameter. The charge passing through the coil is

• A. $\frac{NBA}{R}$
• B. $\frac{\sqrt{3}NBA}{2R}$
• C. $\frac{NBA}{\sqrt{2}R}$
• D. $\frac{2NBA}{R}$

Answer 1

The correct option is D $\frac{2NBA}{R}$

The emf induced in the coil is given by $\frac{d\varphi }{dt}$.

The current passing through the circuit thus becomes $i=\frac{\frac{d\varphi }{dt}}{R}$.

Hence the total charge that passed through the current integrator=$\int idt$

$=\frac{1}{R}\int \frac{d\varphi }{dt}dt$

$=\frac{\Delta \varphi }{R}$

$=\frac{NBA-(-NBA)}{R}$

$=\frac{2NBA}{R}$