IB · D · data analysis

Fields · Question 7

Fields · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand: demanding
Marks: 10
Topics: 1
Answer: Complete

Figure 4A long straight wire is drawn vertically and labelled 'long straight wire'. An arrow drawn along the wire and labelled I gives the direction of the current in it. To the right of the wire, at the same height, a small rectangle labelled 'magnetic field probe' has its near face towards the wire, and a dimension line running perpendicular from the wire to that face is labelled r. A dashed outline of the probe, drawn further to the right at the same height, carries the note 'probe moved to other values of r'.

data analysis10 marks

A student measures the magnetic flux density B at various perpendicular distances r from a long straight wire carrying a steady current I. Theory predicts B = μ₀I/(2πr).

The student's processed data
r / m	0.020	0.025	0.040	0.050	0.100
B / μT	50.0	40.0	25.0	20.0	10.0
1/r / m⁻¹	50.0	40.0	25.0	20.0	10.0

(a)
Explain Explain why a graph of B against 1/r is plotted rather than a graph of B against r.
2 marks
(b)
Determine Determine the gradient of the line, and hence determine the current in the wire.
4 marks
(c)
Suggest The student's measurements at the largest distances scatter more about the line than those close to the wire. Suggest why.
2 marks
(d)
Outline Outline one systematic error that would make every value of B too large, and state how it would show up on the graph.
2 marks

Your working or explanation

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Answer overviewKey answer: B is inversely proportional to r, so a graph of B against r is a curve from which no constant can be read plotting against 1/r linearises the relationship, so the gradient gives μ₀I/(2π) directly and the straightness of the line tests the inverse proportionality gradient = (50.0 − 10.0) × 10⁻⁶ / (50.0 − 10.0) = 1.0 × 10⁻⁶ T m

(a)

2 marks

Explain Explain why a graph of B against 1/r is plotted rather than a graph of B against r.

How to approach it

Read the data before explaining it. Quote the relevant values or trend, show the comparison or calculation, and then connect that numerical evidence to the physical conclusion—including uncertainty or anomalies when they matter.

1
B is inversely proportional to r, so a graph of B against r is a curve from which no constant can be read
2
plotting against 1/r linearises the relationship, so the gradient gives μ₀I/(2π) directly and the straightness of the line tests the inverse proportionality

(b)

4 marks

Determine Determine the gradient of the line, and hence determine the current in the wire.

How to approach it

1
gradient = (50.0 − 10.0) × 10⁻⁶ / (50.0 − 10.0) = 1.0 × 10⁻⁶ T m
2
A plot of B against 1/r has gradient = μ₀I/(2π).
3
I = 2π × 1.0 × 10⁻⁶ / (4π × 10⁻⁷)
4
I = 5.0 A

(c)

2 marks

Suggest The student's measurements at the largest distances scatter more about the line than those close to the wire. Suggest why.

How to approach it

1
the field is weakest at large r, so the reading is a smaller fraction of the probe's full scale and the percentage uncertainty in each reading is larger
2
the Earth's magnetic field and any stray fields are a larger fraction of the measured value at those distances

(d)

2 marks

Outline Outline one systematic error that would make every value of B too large, and state how it would show up on the graph.

How to approach it

1
the probe not being zeroed before the measurements, or the Earth's field component along the probe not being subtracted, would add a constant to every reading
2
the line would still be straight but would not pass through the origin — it would have a positive intercept on the B axis

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