Question

A flat coil, C, of n turns, area A and resisitance R is placed in a uniform magnetic field of magnitude B. The plane of the coil is initially perpendicular to B. If the coil is rotated by an angle about the axis XY, charge of amount Q flows through it.

• A. If $\theta ={90}^o,Q=\frac{BAn}{R}$.
• B. If $\theta ={180}^o,Q=\frac{BAn}{R}$.
• C. If $\theta ={180}^o,Q=0$.
• D. If $\theta ={360}^o,Q=0$.

Answer 1

Answer: (A), (C), (D)

If $\theta ={90}^o,Q=\frac{BAn}{R}$.
If $\theta ={180}^o,Q=0$.
If $\theta ={360}^o,Q=0$.

Coil of N turns:

Magnetic Flux, $\varphi =BAncos\left(\theta \right)$

Induced EMF, $E=\frac{d\varphi }{dt}=BAnsin\left(\theta \right)\frac{\Delta \theta }{\Delta t}$

Current induced $=\frac{E}{R}=\frac{BAn}{R}sin\left(\theta \right)\frac{\Delta \theta }{\Delta t}$

Total Charge flowing $=I\Delta t=\frac{BAn}{R}sin\left(\theta \right)\Delta \theta$
$\Delta \theta ={\theta }_{final}-{\theta }_{init}=\theta$

$Q=\frac{BAn}{R}sin\left(\theta \right)\theta$