A student conducted two experiments to investigate the magnetic field strength, B (measure… — ACT

A student conducted two experiments to investigate the magnetic field strength, $B$ (measured in microtesla, $\mu\text{T}$ ), surrounding a straight, current-carrying wire. In Experiment 1, the student measured the magnetic field at varying distances, $r$ , from the wire while holding the current constant. In Experiment 2, the student measured the magnetic field at a fixed distance while varying the current, $I$ . The results of these experiments are shown in Table 1 and Table 2.

### Table 1

Trial	Current $I$ ( $\text{A}$ )	Distance $r$ ( $\text{m}$ )	Magnetic Field $B$ ( $\mu\text{T}$ )
1	2.0	0.10	4.0
2	2.0	0.20	2.0
3	2.0	0.40	1.0

### Table 2

Trial	Distance $r$ ( $\text{m}$ )	Current $I$ ( $\text{A}$ )	Magnetic Field $B$ ( $\mu\text{T}$ )
4	0.10	1.0	2.0
5	0.10	2.0	4.0
6	0.10	3.0	6.0

Based on the results of the experiments, if the student conducts a new trial with a current of $4.0\text{ A}$ at a distance of $0.20\text{ m}$ from the wire, what is the predicted magnetic field strength $B$ ?

A
$1.0\ \mu\text{T}$
B
$2.0\ \mu\text{T}$
$4.0\ \mu\text{T}$ Answer
D
$16.0\ \mu\text{T}$

Answer

4.0\ \mu\text{T}

The correct answer is

4.0\ \mu\text{T}

. According to Table 1, when current is held constant, doubling the distance from

0.10\text{ m}

0.20\text{ m}

halves the magnetic field strength from

4.0\ \mu\text{T}

2.0\ \mu\text{T}

, demonstrating an inverse proportionality. According to Table 2, when distance is held constant, doubling the current from

1.0\text{ A}

2.0\text{ A}

doubles the magnetic field strength from

2.0\ \mu\text{T}

4.0\ \mu\text{T}

, demonstrating a direct proportionality. Starting from Trial 2 where

r = 0.20\text{ m}

I = 2.0\text{ A}

, and

B = 2.0\ \mu\text{T}

, doubling the current to

4.0\text{ A}

while keeping the distance constant at

0.20\text{ m}

doubles the field strength to

4.0\ \mu\text{T}

Step-by-Step Solution

Determine the relationship between distance

r

and magnetic field

B

B

is inversely proportional to

r

(

B \propto 1/r

According to Table 1, with current constant, doubling the distance from

0.10\text{ m}

0.20\text{ m}

reduces the magnetic field from

4.0\ \mu\text{T}

2.0\ \mu\text{T}

Determine the relationship between current

I

and magnetic field

B

B

is directly proportional to

I

(

B \propto I

According to Table 2, with distance constant, doubling the current from

1.0\text{ A}

2.0\text{ A}

doubles the magnetic field from

2.0\ \mu\text{T}

4.0\ \mu\text{T}

Calculate the predicted magnetic field for a new trial with

I = 4.0\text{ A}

and

r = 0.20\text{ m}

using a baseline trial.

B = 4.0\ \mu\text{T}

Starting from Trial 2 (

I = 2.0\text{ A}

r = 0.20\text{ m}

B = 2.0\ \mu\text{T}

), the distance matches the target trial. Since current is doubled from

2.0\text{ A}

4.0\text{ A}

, and

B

is directly proportional to

I

, we multiply the field by

2

2.0\ \mu\text{T} \times 2 = 4.0\ \mu\text{T}

Key Concept

Direct and Inverse Proportionality

Estimated Time:1m 30s

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