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Inverse Square Law Problems

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Inverse Square Law Problems

For an ideal point source in a uniform medium, use Q ∝ 1/r². For power spread uniformly in all directions, use I = P/(4πr²). Show equations, substitutions and units. Assume negligible absorption unless stated.

Mission briefing: measure the signal

A field team is checking how signals change with distance. Treat each source as a point source and each measurement as being made in the far field.

1.A detector is moved from 2.0 m to 6.0 m from a point source. By what factor does the measured intensity change? Choose the correct result.

It becomes 3 times as large
It becomes 1/3 as large
It becomes 1/9 as large
It becomes 9 times as large

2.A point source produces an intensity of 72 W m⁻² at 4.0 m. Calculate its intensity at 12.0 m. Include the inverse-square ratio in your working.

3.A source's intensity is measured as 80 W m⁻². At what distance from the source will it be 5.0 W m⁻² if the first measurement was taken 3.0 m away? Show how you find the distance ratio.

4.A small isotropic lamp emits 24 W of radiant power. Calculate the irradiance at a detector 3.0 m away using I = P/(4πr²). Give your answer in W m⁻² to two significant figures.

5.At 5.0 m, a point sound source produces an intensity of 2.4 × 10⁻³ W m⁻². Calculate the source power, assuming sound spreads uniformly in all directions and there are no losses.

6.Two identical lamps each produce 36 lux at a detector when 2.0 m away. One lamp is moved to 4.0 m while the other stays at 2.0 m. Find the new total illuminance, assuming the readings add.

7.At a planet's surface radius R, gravitational acceleration is 9.80 m s⁻². The planet's mass stays constant, but its radius increases to 1.20R. Calculate the new surface gravity to three significant figures.

8.A point charge produces an electric field magnitude E₀ at distance r. What is the field magnitude at distance 0.25r? State the ratio and explain briefly.

9.True or false? If intensity from a point source falls to one quarter of its original value, the detector must be twice as far from the source. Justify your answer with a proportional relationship.

TrueFalse

10.A student says, “At twice the distance, a point source's intensity is half as great.” Identify the error and correct the statement using a numerical ratio.

11.A space probe records a signal intensity of 9.0 × 10⁻⁶ W m⁻² at 15 km from an isotropic transmitter. Estimate the intensity at 45 km. State one condition needed for this inverse-square estimate to be valid.