First slide

Magnetic flux and induced emf

Question

The magnetic field of an electromagnetic wave obeys the relation in a certain region is $B = 10^{- 12} \sin (1 \times 10^{6} t)$ in tesla, where $' t'$ is the time. Then, the induced $emf$ , in a 100 turns in coil of area ${10cm}^{2}$ oriented perpendicular to the field is

Moderate

A

$- 2 \times 10^{- 7} \cos (1 \times 10^{6} t) V$
B

$- 1 \times 10^{- 7} \cos (1 \times 10^{6} t) V$
C

$- 1.5 \times 10^{- 7} \cos (1 \times 10^{6} t) V$
D

$- 3 \times 10^{- 7} \cos (1 \times 10^{6} t) V$

Solution

$Induced emf e= \frac{- d ϕ}{d t} = - N \frac{d (B A \cos θ)}{d t} [h e r e θ = 0^{o} a s f i e l d i s n o r m a l t o c o i l] \Rightarrow e = - N A \frac{d (B)}{d t} \Rightarrow e = - N A \frac{d (B_{o} \sin ω t)}{d t} \Rightarrow e = - N A B_{o} ω \cos ω t \Rightarrow e = - 100 \times 10 \times 10^{- 4} \times 10^{- 12} \times 10^{6} \cos (10^{6} t) \Rightarrow e = - 10^{- 7} \cos (10^{6} t)$

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