A wire of length 30cm is moved with a speed of 2$ms^{-1}$ at right angles to a magnetic field of flux density 0.4T. calculate the emf induced in the wire

Analyze the question

A straight wire moves perpendicular to a magnetic field, so it cuts the field lines and an emf is induced across its ends (motional emf).

Given:

• Length, l = 30 cm = 0.30 m (convert to metres first)
• Speed, v = 2 m/s
• Flux density, B = 0.4 T
• Angle between motion and field = 90°

Concept

For a conductor moving through a magnetic field:

E = B l v sin θ

At right angles, sin 90° = 1, so:

E = B l v

Solution

E = 0.4 × 0.30 × 2

E = 0.4 × 0.6

E = 0.24 V

Answer

The emf induced is 0.

Tip

Always convert length to metres before substituting. If you forget and use 30 instead of 0.30, you get 24 V (option D), which is a common trap. Also remember that sin θ = 1 when the wire moves at right angles to the field, so the formula reduces to E = Blv.