A flat coil , of n turns , area A and resistance R is placed in a uniform magnetic field - Physics - Electromagnetic Induction

Question

A flat coil , of n turns , area A and resistance 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
O about the axis XY , charge of amout Q flows
through it
a if O = 90o, Q = BAn/R
b if O = 180o, Q = BAn/R
c if O = 180o, Q = 0
d if O = 360o, Q = 0
Which options are correct

Himanshu · Accepted Answer

Charge flowing in the circuit will be given by:

$\frac{| Δ Φ |}{R}, Δ Φ = c h a n g e i n f l u x a n d R i s t h e r e s i s \tan c e$

$Φ = B A n \cos θ, w h e r e θ i s t h e a n g l e b e t w e e n m a g n e t i c f i e l d a n d p l a n e o f c o i l . Φ_{i n i t i a l} = B A n \cos 0 = B A n Φ_{f i n a l} = B A n \cos (α), w h e r e α i s t h e a n g l e b y w h i c h i t i s r o t a t e d α = 90^{°} Φ_{f i n a l} = 0 Q = \frac{| Δ Φ |}{R} = \frac{B A n}{R} α = 180^{°} Φ_{f i n a l} = B A n \cos π = - B A n Q = \frac{| Δ Φ |}{R} = \frac{2 B A n}{R} α = 360^{°} Φ_{f i n a l} = B A n \cos 2 π = B A n Q = \frac{| Δ Φ |}{R} = 0$

Hence, options (a), and (d) are correct.