SME
Engineering Electromagnetics
Maxwell's equations
Use this for “Find B 2 cm from a long wire carrying 10 A.”
Diagram
B
=
μ₀
I
2πr
=
1.26 ×
10
-6
×
10
2π × 0.02
B
=
1 ×
10
-4
T
H
=
I
2πr
=
79.6
A/m
This is an example. Type your own values to start a new problem.
H (A/m)
=
I (A)
2π
r (cm)
B (T)
=
μ₀
H (A/m)
Formulas
H
=
I
2π ×
r
79.5775
=
10
2π × 0.02
B
=
4π
×
10
-7
×
H
1 ×
10
-4
=
4π
×
10
-7
×
79.5775
Formulas are worked in m. The step-by-step shows the conversions.
Assumptions
•
A long straight wire; r is measured from its center to a point outside it.
•
Ampère’s law round a circle of radius r: H × 2πr = I, so H = I ÷ (2πr).
•
In air or another nonmagnetic material, B = μ₀H with μ₀ = 4π × 10⁻⁷ H/m.
Step-by-step
WE KNOW
I = 10 A, r = 2 cm
FIND
magnetic field intensity (H), magnetic flux density (B)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to m).
r = 2 cm = 0.02 m (1 m = 100 cm)
Step 2 · Find magnetic field intensity (H)
Use H = I ÷ (2π × r)
Ampère’s law: the current is shared evenly round the circle’s length 2πr.
H
=
10
2π × 0.02
H
=
79.5775
A/m
Step 3 · Find magnetic flux density (B)
Use B = 4π × 10⁻⁷ × H
In
a
nonmagnetic
material,
B
is
μ₀
times
H
.
B
=
4π
×
10
-7
×
79.5775
B
=
1 ×
10
-4
T
Check
Put the numbers back in. Both sides should match.
79.5775
=
10
2π × 0.02
✓
1 ×
10
-4
=
4π
×
10
-7
×
79.5775
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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