A metallic ring of area `25 cm^(2)` is placed perpendicular to a magnetic field of `0.2 T`.Its is removed from the field in `0.2 s`.Find the average `emf` produced in the ring during this time.

Answer

To find the average EMF produced in the metallic ring when it is removed from the magnetic field, we can follow these steps:

### Step 1: Understand the concept of magnetic flux
Magnetic flux (Φ) through a surface is given by the product of the magnetic field (B) and the area (A) of the surface perpendicular to the field:
\[ \Phi = B \cdot A \]

### Step 2: Convert the area from cm² to m²
The area of the ring is given as \(25 \, \text{cm}^2\). We need to convert this to square meters:
\[ A = 25 \, \text{cm}^2 = 25 \times 10^{-4} \, \text{m}^2 = 0.0025 \, \text{m}^2 \]

### Step 3: Calculate the initial magnetic flux (Φ_i)
Using the formula for magnetic flux, we can calculate the initial flux when the ring is in the magnetic field:
\[ \Phi_i = B \cdot A = 0.2 \, \text{T} \cdot 0.0025 \, \text{m}^2 = 0.0005 \, \text{Wb} \, (\text{Weber}) \]

### Step 4: Determine the final magnetic flux (Φ_f)
Since the ring is removed from the magnetic field, the final magnetic flux is:
\[ \Phi_f = 0 \, \text{Wb} \]

### Step 5: Calculate the change in magnetic flux (ΔΦ)
The change in magnetic flux (ΔΦ) is given by:
\[ \Delta \Phi = \Phi_f - \Phi_i = 0 - 0.0005 = -0.0005 \, \text{Wb} \]

### Step 6: Calculate the average induced EMF (ε_avg)
The average induced EMF can be calculated using the formula:
\[ \epsilon_{\text{avg}} = -\frac{\Delta \Phi}{\Delta t} \]
Where Δt is given as \(0.2 \, \text{s}\):
\[ \epsilon_{\text{avg}} = -\frac{-0.0005 \, \text{Wb}}{0.2 \, \text{s}} = \frac{0.0005}{0.2} = 0.0025 \, \text{V} = 2.5 \times 10^{-3} \, \text{V} \]

### Final Answer
The average EMF produced in the ring during this time is:
\[ \epsilon_{\text{avg}} = 2.5 \times 10^{-3} \, \text{V} \]

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