Dynamically Induced EMF Calculator – e = Blv sin θ

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Dynamically Induced EMF Calculator

e = B l v sin θ • Conductor cutting a magnetic field • Fleming’s right-hand rule

When a conductor moves in a stationary magnetic field and cuts the flux, an emf is induced in it — a dynamically induced emf. Its value is e = B l v sin θ, where θ is the angle between the direction of motion and the field. Only the part of the velocity perpendicular to the field, v sin θ, cuts flux.

📘 How to Use (tap to hide / show)

1. 1Choose what to find: emf e, flux density B, length l, velocity v or angle θ.
2. 2Enter the other values and pick their units (cm, km/h, mT…) — the calculator converts them to SI units.
3. 3Set the angle θ between v and B with the box or the slider. The diagram shows it immediately.
4. 4Click ⚡ Calculate to get the answer, the step-by-step working and the emf direction (⊗ / ⊙).

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What Do You Want to Find?

2

Enter the Known Values

Field direction:

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Diagram – Conductor Moving in the Field

Magnetic field B Velocity v v sin θ (cuts flux) v cos θ (no emf) ⊗ current into page   ⊙ out of page

✓ Result

Step-by-step Solution

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Fleming’s Right-Hand Rule and Special Cases

Fleming’s Right-Hand Rule (generator rule)

Stretch the thumb, first finger and second finger of the right hand mutually at right angles:

• Thumb → direction of Motion of the conductor
• First finger → direction of Field (N to S)
• Second finger → direction of induced Current / emf

Special cases of e = B l v sin θ

Angle θ	Motion	Induced emf
0° or 180°	Parallel to the field	e = 0 (no flux cut)
90°	Perpendicular to the field	e = B l v (maximum)
Any other θ	At an angle	e = B l v sin θ

Statically vs dynamically induced: in a dynamically induced emf the conductor moves (generator); in a statically induced emf nothing moves and the flux itself changes (self-induced, mutually induced — transformer).

Note: B in tesla (1 T = 1 Wb/m²), l = active length of the conductor inside the field in metres, v in m/s. θ is measured from the direction of B to the direction of v, anticlockwise, from 0° to 360° when finding e (180°–360° means the conductor moves the other way, so the emf reverses). When finding B, l, v or θ, enter the size of the emf and an angle between 0° and 180°.