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A2 Daily A Level Physics question

2026-05-26 OCR A Fields: Gravitational, Electric & Magnetic (M5/M6) 6.2 Electric fields (point charges): E ∝ 1/r² with distance 2.2 Practical skills: graphical analysis; straight-line testing; proportionality checks

In a lab, a student measures the electric field strength E at various distances r from the centre of a small isolated charged sphere. They want to test whether E follows an inverse‑square dependence on r (assume no background field). Which statement must be true if that model is correct?

  1. A Plot E against r to get a straight line through the origin; doubling r would reduce E to half.
  2. B Plot E against 1/r to get a straight line through the origin; increasing r by a factor of 1.5 would reduce E to about 0.67 of its value.
  3. C Plot E against 1/r² to get a straight line through the origin with gradient equal to the constant of proportionality; increasing r by a factor of 1.5 would reduce E to about 0.44 of its value. (correct)
  4. D Plot 1/E against r² to get a straight line through the origin with gradient equal to the constant of proportionality; doubling r would reduce E to half.

Answer

The correct answer is C.

Correct: C — Plot E against 1/r² to get a straight line through the origin with gradient equal to the constant of proportionality; increasing r by a factor of 1.5 would reduce E to about 0.44 of its value. A E versus r is not linear for an inverse‑square, and doubling r would quarter E, not halve it. B A straight line of E against 1/r corresponds to a 1/r model; the 0.67 factor belongs to 1/r, not 1/r². C For E proportional to 1/r², E versus 1/r² is linear through the origin with gradient equal to the proportionality constant, and increasing r by 1.5 gives a factor 1/(1.5)² ≈ 0.44. D Although 1/E versus r² is linear, its gradient is the reciprocal of the proportionality constant, and doubling r would quarter E, not halve it.