Magnetic flux passing through a coil is initially `4xx 10^-4` Wb. It reduces to 10% of its original value in t second. If the emf induced is 0.72 mV then t in second is

Options

A. `0.3`
B. `0.4`
C. `0.5`
D. `0.6`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Identify the initial magnetic flux
The initial magnetic flux (\( \Phi_0 \)) is given as:
\[ \Phi_0 = 4 \times 10^{-4} \, \text{Wb} \]

### Step 2: Calculate the final magnetic flux
The final magnetic flux (\( \Phi \)) is 10% of the initial value. Therefore:
\[ \Phi = 0.1 \times \Phi_0 = 0.1 \times (4 \times 10^{-4}) = 4 \times 10^{-5} \, \text{Wb} \]

### Step 3: Calculate the change in magnetic flux
The change in magnetic flux (\( \Delta \Phi \)) can be calculated as:
\[ \Delta \Phi = \Phi_0 - \Phi = (4 \times 10^{-4}) - (4 \times 10^{-5}) = 4 \times 10^{-4} - 0.4 \times 10^{-4} = 3.6 \times 10^{-4} \, \text{Wb} \]

### Step 4: Use the formula for induced EMF
The induced electromotive force (EMF) is given as:
\[ \text{EMF} = \frac{\Delta \Phi}{\Delta t} \]
Given that the EMF is \( 0.72 \, \text{mV} = 0.72 \times 10^{-3} \, \text{V} \), we can set up the equation:
\[ 0.72 \times 10^{-3} = \frac{3.6 \times 10^{-4}}{t} \]

### Step 5: Solve for time \( t \)
Rearranging the equation to solve for \( t \):
\[ t = \frac{3.6 \times 10^{-4}}{0.72 \times 10^{-3}} \]
Calculating this gives:
\[ t = \frac{3.6}{0.72} \times 10^{-1} = 5 \times 10^{-1} = 0.5 \, \text{s} \]

### Conclusion
Thus, the time \( t \) is:
\[ \boxed{0.5 \, \text{s}} \]