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Question #42921

Difficulty: 8/10 | 🟢 Free

The Question

An isotropic point source emitting monochromatic light of total power $P$ is located at the origin $(0,0,0)$ in a vacuum. A perfectly absorbing, rigid cylindrical surface is defined by the equation $x^2 + y^2 = R^2$ and spans the region $0 \le z \le H$ . If $c$ is the speed of light in vacuum, what is the magnitude of the net force exerted by the electromagnetic radiation on this cylindrical surface?

Options

A.
$\frac{P}{4c} \frac{H^2}{R^2+H^2}$
B.
$\frac{P}{2c} \frac{H}{\sqrt{R^2+H^2}}$
C.
$\frac{P}{4c} \frac{R^2}{R^2+H^2}$
D.
$\frac{P}{2c} \frac{H^2}{R^2+H^2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Flux and Surface Geometry|Intensity and Photon Flux

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between total absorbed power (energy flux) and net radiation force (momentum flux) in a non-planar electromagnetic field.

A common 'lethal mistake' is calculating the total power $\Phi$ absorbed by the cylinder and simply dividing by $c$ to find the force ( $F = \Phi/c$ ).

This incorrectly assumes that the momentum vectors of all absorbed photons are parallel to the net force direction.

Students must recognize that the Poynting vector is radially outward from the point source, requiring them to project the momentum transfer onto the z-axis and integrate the geometric factors ( $\cos\theta$ ) correctly.

Alternatively, students can elegantly solve this using conservation of momentum by subtracting the momentum flux escaping through the top circular cap from the total momentum flux emitted into the upper hemisphere.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Flux and Surface Geometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free