Problem Statement
A long straight wire carries $I = 6\,\text{A}$. Find the magnetic field at $r = 10\,\text{cm}$ from the wire.
Given Information
- $I = 6\,\text{A}$
- $r = 0.10\,\text{m}$
- $\mu_0 = 4\pi\times10^{{-7}}\,\text{{T m A}}^{{-1}}$
Physical Concepts & Formulas
Ampere’s law for an infinite straight wire: $B\cdot2\pi r = \mu_0 I$, giving $B = \mu_0 I/(2\pi r)$. The field curls around the wire by the right-hand rule.
- $B = \mu_0 I/(2\pi r)$ — Ampere’s law for straight wire
Step-by-Step Solution
Step 1 — Ampere’s law: $B\cdot2\pi r = \mu_0 I \Rightarrow B = \mu_0 I/(2\pi r)$
Step 2 — Substitute: $$B = \frac{4\pi\times10^{-7}\times6}{2\pi\times0.10}$$
Step 3 — Compute: $$B = 1.2e-05\,\text{T}$$
Worked Calculation
$$B = \frac{4\pi\times10^{-7}\times6}{2\pi\times0.10} = 1.2e-05\,\text{T}$$
Answer
$$\boxed{B = 1.2e-05\,\text{T}}$$
The field 1.2e-05 T from a 6 A wire at 10 cm. This curls around the wire and can deflect compass needles — as Oersted famously observed in 1820, linking electricity and magnetism.
Physical Interpretation
The field 1.2e-05 T from a 6 A wire at 10 cm. This curls around the wire and can deflect compass needles — as Oersted famously observed in 1820, linking electricity and magnetism.
The magnitude of this result is physically reasonable and consistent with the expected order of magnitude for this class of problem. Comparing with standard values from physical tables confirms we are in the correct range.
This problem illustrates a fundamental principle that appears throughout physics: small changes in one parameter can lead to measurable, predictable changes in the observable quantity. Understanding this relationship is key to experimental design.
Note that the result depends on the square (or square root) of the key variable — this nonlinear dependence is characteristic of many physics phenomena and means that doubling the parameter does not simply double the result. Students should always check dimensional consistency and order-of-magnitude before accepting any numerical answer.
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