Question

The radiation produced by a 100 W bulb has the following property

• A. The radiation is in the form of an electromagnetic wave which carries energy but not momentum
• B. The radiation is in the form of an electromagnetic wave which carries momentum but not energy
• C. The radiation is in the form of an electromagnetic wave which carries both energy and momentum
• D. The radiation neither carries energy nor momentum
• E. The intensity of radiation is independent of the distance from source

Hint:

If light had no momentum, "Solar Sails" would not work in space. The fact that light can push objects is proof that it carries momentum alongside energy.

Answer 1

The Correct Option is C

Concept:
Electromagnetic (EM) waves are oscillations of electric and magnetic fields that transport energy through space. According to Maxwell's theory and quantum mechanics, these waves also possess linear momentum.

Step 1: Energy Transport.
The power of the bulb (100 W) represent the rate of energy transfer ($J/s$). This energy is carried by photons/EM waves away from the filament.

Step 2: Momentum Transport.
The linear momentum ($p$) of an electromagnetic wave is related to the energy ($U$) it carries by the relation: \[ p = \frac{U}{c} \] where $c$ is the speed of light. Because light carries momentum, it exerts a tiny force known as radiation pressure when it strikes a surface.

Step 3: Evaluating Intensity.
Intensity ($I$) is power per unit area. For a point source like a bulb, energy spreads spherically: \[ I = \frac{P}{4\pi r^2} \] Since $I \propto 1/r^2$, statement (E) is incorrect as intensity depends heavily on the distance from the source.