First slide

Magnetic flux and induced emf

Question

The magnetic field of an electromagnetic wave , obeys the relation in a certain region , is $B = 10^{- 12} \sin (5 \times 10^{6} t) T$ , where $t$ is the time . Then the induced $emf$ , in a 300 turns coil of area ${20cm}^{2}$ oriented perpendicular to the field is

Moderate

A

$- 2 \times 10^{- 5} \cos (5 \times 10^{6} t) V$
B

$- 3 \times 10^{- 6} \cos (5 \times 10^{6} t) V$
C

$- 2.5 \times 10^{- 6} \cos (5 \times 10^{6} t) V$
D

$- 3.3 \times 10^{- 6} \cos (5 \times 10^{6} t) V$

Solution

$Induced emf : e= \frac{- d ϕ}{d t} = - N \frac{d (B A \cos θ)}{d t}$
$\Rightarrow e = - N A \frac{d B}{d t} [C o i l i s p e r p e n d i c u l a r t o f i e l d ∴ \cos θ = 1] \Rightarrow e = - N A \frac{d (B_{o} \sin ω t)}{d t} \Rightarrow e = - B_{o} A N ω \cos ω t \Rightarrow e = - 10^{- 12} \times 20 \times 10^{- 4} \times 3 \times 10^{2} \times 5 \times 10^{6} \cos (5 \times 10^{6} t) \Rightarrow e = - 3 \times 10^{- 6} \cos (5 \times 10^{6} t)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App