The magnetic flux in a coil of 100 turns increase by `12 xx10^(3)` Maxwell in 0.2 s due to the motion of a magnet . The emf induced in the coil will be :-

Options

A. 0.06 V
B. 0.6 V
C. 6V
D. 60 V

Answer

To find the induced EMF in the coil, we can follow these steps:

### Step 1: Understand the formula for induced EMF
The induced EMF (ε) in a coil can be calculated using the formula:
\[ \varepsilon = -n \frac{d\Phi}{dt} \]
where:
- \( n \) is the number of turns in the coil,
- \( \frac{d\Phi}{dt} \) is the rate of change of magnetic flux.

### Step 2: Identify the given values
From the problem, we have:
- Number of turns, \( n = 100 \)
- Change in magnetic flux, \( \Delta \Phi = 12 \times 10^3 \) Maxwell
- Time interval, \( \Delta t = 0.2 \) s

### Step 3: Convert Maxwell to Weber
We need to convert the change in magnetic flux from Maxwell to Weber. The conversion is:
\[ 1 \text{ Maxwell} = 10^{-8} \text{ Weber} \]
Thus,
\[ \Delta \Phi = 12 \times 10^3 \text{ Maxwell} = 12 \times 10^3 \times 10^{-8} \text{ Weber} = 12 \times 10^{-5} \text{ Weber} \]

### Step 4: Calculate the rate of change of magnetic flux
Now we can calculate \( \frac{d\Phi}{dt} \):
\[ \frac{d\Phi}{dt} = \frac{\Delta \Phi}{\Delta t} = \frac{12 \times 10^{-5} \text{ Weber}}{0.2 \text{ s}} = 60 \times 10^{-5} \text{ Weber/s} = 6 \times 10^{-4} \text{ Weber/s} \]

### Step 5: Substitute values into the EMF formula
Now we can substitute the values into the EMF formula:
\[ \varepsilon = n \frac{d\Phi}{dt} = 100 \times 6 \times 10^{-4} = 6 \times 10^{-2} \text{ V} \]

### Step 6: Final answer
Thus, the induced EMF in the coil is:
\[ \varepsilon = 0.06 \text{ V} \]