A flat square plate with side length d serves as a detector for the radiations emitted by particle. The particle emits the radiations uniformly in all directions.

Consider the line joining the points A and C as shown. C is corner of square. A is the point directly above the opposite corner. When particle is placed at point B (halfway between A and C) then fraction of total energy emitted by particle, detected by square plate is $f_{B}$ . When particle is placed at a point infinitesimally close to C (along line joining AC), corresponding fraction is $f_{C}$ . The value of $\frac{f_{B}}{f_{C}}$ is $\frac{4}{n}$ . Find value of n.

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answer is 7.

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Detailed Solution

$f_{B} = \frac{1}{6} a n d f_{C} = \frac{7}{24} \Rightarrow \frac{f_{B}}{f_{C}} = \frac{1}{6 \times \frac{7}{24}} = \frac{24}{6 \times 7} = \frac{4}{7}$

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