An electromagnetic wave of intensity `1400. (W) / (m)^(2)` falls on a metal surface of area `1.5m^2` and is completely absorbed by it. Find out the force (in `mu N` ) exerted by the beam.

Answer

To find the force exerted by an electromagnetic wave on a metal surface that completely absorbs the wave, we can use the relationship between intensity, area, and force. Here’s a step-by-step solution:

### Step 1: Understand the given values
- **Intensity (I)** = 1400 W/m²
- **Area (A)** = 1.5 m²

### Step 2: Use the formula for force exerted by the electromagnetic wave
The force (F) exerted by an electromagnetic wave on a surface that completely absorbs it can be calculated using the formula:

\[ F = \frac{I \cdot A}{c} \]

where:
- \(I\) is the intensity of the wave,
- \(A\) is the area of the surface,
- \(c\) is the speed of light in vacuum (approximately \(3 \times 10^8\) m/s).

### Step 3: Substitute the known values into the formula
Now, plug in the values into the formula:

\[ F = \frac{1400 \, \text{W/m}^2 \times 1.5 \, \text{m}^2}{3 \times 10^8 \, \text{m/s}} \]

### Step 4: Calculate the numerator
Calculate the product of intensity and area:

\[ 1400 \times 1.5 = 2100 \, \text{W} \]

### Step 5: Calculate the force
Now substitute the value back into the formula:

\[ F = \frac{2100 \, \text{W}}{3 \times 10^8 \, \text{m/s}} \]

Calculating this gives:

\[ F = 7 \times 10^{-6} \, \text{N} \]

### Step 6: Convert the force into micro Newtons
Since \(1 \, \text{N} = 10^6 \, \mu\text{N}\), we convert the force:

\[ F = 7 \times 10^{-6} \, \text{N} = 7 \, \mu\text{N} \]

### Final Answer
Thus, the force exerted by the beam is **7 micro Newtons (μN)**.

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