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Question: Magnetic flux passing through a coil is initially $4 \times 10^{-4}$ Wb. It reduces to 10% of origin...

Magnetic flux passing through a coil is initially 4×10−44 \times 10^{-4} Wb. It reduces to 10% of original value in 't' seconds. If the e.m.f. induced is 0.72 mV then 't' in seconds is

A

0.3

B

0.4

C

0.5

D

0.6

Answer

0.5 seconds

Explanation

Solution

The initial magnetic flux is given as:

Φi=4×10−4 Wb.\Phi_i = 4\times10^{-4}\,\text{Wb}.

The final flux is 10% of the initial value:

Φf=0.1×(4×10−4)=4×10−5 Wb.\Phi_f = 0.1\times (4\times10^{-4}) = 4\times10^{-5}\,\text{Wb}.

The change in flux is:

ΔΦ=Φi−Φf=4×10−4−4×10−5=3.6×10−4 Wb.\Delta\Phi = \Phi_i - \Phi_f = 4\times10^{-4} - 4\times10^{-5} = 3.6\times10^{-4}\,\text{Wb}.

Using Faraday’s law, the induced emf is:

E=∣ΔΦ∣t.\mathcal{E} = \frac{|\Delta\Phi|}{t}.

Given that the induced emf is 0.72 mV=0.72×10−3 V0.72\,\text{mV} = 0.72\times10^{-3}\,\text{V}, we can solve for tt:

t=3.6×10−40.72×10−3=0.5 s.t = \frac{3.6\times10^{-4}}{0.72\times10^{-3}} = 0.5\,\text{s}.