Problem Statement
Find the magnetic field at the centre of a circular loop of radius $R = 1\,\text{cm}$ carrying current $I = 8\,\text{A}$.
Given Information
- $R = 0.01\,\text{m}$
- $I = 8\,\text{A}$
- $\mu_0 = 4\pi\times10^{{-7}}\,\text{{T m A}}^{{-1}}$
Physical Concepts & Formulas
By Biot–Savart law, every current element of the loop contributes a field at the centre in the same direction. Integrating: $B = \mu_0 I/(2R)$.
- $B = \mu_0 I/(2R)$ — centre of circular loop
Step-by-Step Solution
Step 1 — Formula: $B = \mu_0 I/(2R)$
Step 2 — Substitute: $$B = \frac{4\pi\times10^{-7}\times8}{2\times0.01}$$
Step 3 — Compute: $$B = 0.000503\,\text{T}$$
Worked Calculation
$$B = \frac{4\pi\times10^{-7}\times8}{2\times0.01} = 0.000503\,\text{T}$$
Answer
$$\boxed{B = 0.000503\,\text{T}}$$
The field 0.000503 T at the centre of this 1 cm radius loop. Helmholtz coil pairs use two such loops to create uniform fields for physics experiments.
Physical Interpretation
The field 0.000503 T at the centre of this 1 cm radius loop. Helmholtz coil pairs use two such loops to create uniform fields for physics experiments.
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