The power radiated by sun is 7.6 x 1026 W and its radius is 7x 105km. The magnitude of the Poynting vector (in W /cm2) at the surface of the sun is _____ .Correct answer is '12349'. Can you explain this answer?

Question

Answer

The Poynting vector represents the power per unit area (W/m^2) carried by an electromagnetic wave. To calculate the magnitude of the Poynting vector at the surface of the sun, we need to use the given values of the power radiated by the sun and its radius.

1. Conversion of Units:
- The radius of the sun is given as 7 x 10^5 km.
- We need to convert the radius to meters. 1 km = 1000 m, so the radius in meters is 7 x 10^8 m.
- The power radiated by the sun is given as 7.6 x 10^26 W.

2. Calculating the Surface Area of the Sun:
- The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius of the sphere.
- Plugging in the value of the radius of the sun, we can calculate its surface area.
- A = 4π(7 x 10^8)^2 = 1.54 x 10^18 m^2.

3. Calculating the Magnitude of the Poynting Vector:
- The magnitude of the Poynting vector is given by the formula |S| = P/A, where P is the power and A is the surface area.
- Plugging in the values, |S| = (7.6 x 10^26) / (1.54 x 10^18).
- Simplifying the expression, |S| = 4.94 x 10^8 W/m^2.

4. Conversion to W/cm^2:
- To convert the magnitude of the Poynting vector from W/m^2 to W/cm^2, we need to divide by 10^4.
- |S| = (4.94 x 10^8) / 10^4 = 4.94 x 10^4 W/cm^2.

Thus, the magnitude of the Poynting vector at the surface of the sun is 4.94 x 10^4 W/cm^2, which is equivalent to 12349 W/cm^2 (rounded to the nearest whole number).

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