SME
Engineering Electromagnetics · Problem type
Faraday’s law: emf in a coil
Use this for “A 100-turn coil of area 0.01 m² sees B rise by 0.2 T in 0.1 s. Find the emf.”
Diagram
ε = NΔΦ/Δt = 100 × 0.002/0.1 = 2 V
Pushing the N pole in, the coil’s current makes its near end an N pole that pushes back (Lenz’s law).
Faster motion or more turns: a bigger emf.
No motion: no current.
Area of each turn A = 0.01 m²
Change in field ΔB = 0.2 T
This is an example. Type your own values to start a new problem.
ΔΦ (Wb)
=
A (m²)
×
ΔB (T)
ε (V)
=
N
×
ΔΦ (Wb)
Δt (s)
Formulas
ΔΦ
=
A
×
ΔB
0.002 = 0.01 × 0.2
ε
=
N
×
ΔΦ
Δt
2
=
100
×
0.002
0.1
Assumptions
•
B is even and square to the coil’s face, so the flux through each turn is Φ = BA.
•
B changes at a steady rate over Δt, so ε = NΔΦ ÷ Δt is the emf all through the change.
•
Lenz’s law gives the sign: the current opposes the change. Only the size of ε is worked here.
Step-by-step
WE KNOW
N = 100, A = 0.01 m², ΔB = 0.2 T, Δt = 0.1 s
FIND
change in flux through each turn (ΔΦ), induced emf (ε)
Step 1 · Find change in flux through each turn (ΔΦ)
Use ΔΦ = A × ΔB
The flux through one turn is BA, so it changes by the area times the change in B.
ΔΦ = 0.01 × 0.2
ΔΦ = 0.002 Wb
Step 2 · Find induced emf (ε)
Use ε = N × ΔΦ ÷ Δt
Faraday’s
law:
each
turn
gets
ΔΦ
Δt
,
and
the
N
turns
in
series
add
up.
ε
=
100
×
0.002
0.1
ε
=
0.2
0.1
ε
=
2
V
Check
Put the numbers back in. Both sides should match.
0.002 = 0.01 × 0.2 ✓
2
=
100
×
0.002
0.1
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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