Question

A conductor of length 0.5 m moves in a uniform magnetic field of density 1.1 T at certain velocity. Find the velocity if the induced voltage in the conductor is 16.5 V and the direction of motion is perpendicular to the field.
1. 30 m/s
2. 60 m/s
3. 40 m/s
4. 50 m/s

Answer 1

Correct Answer - Option 1 : 30 m/s

Concept:

When a straight conductor is moved through a magnetic field an e.m.f. is induced between its ends. This movement must be in such a direction that the conductor cuts through the lines of magnetic flux, and will be a maximum when it moves at right angles to the field.

Let the length of the conductor be L and the flux density of the field be B.

If the conductor moves with velocity v at right angles to the field, then the flux cut per second will be BvL (since the conductor will sweep out an area vL every second).

But the rate of cutting flux is equal to the e.m.f. induced in the conductor. Therefore,

E = BLv

If the conductor cuts through the flux at an angle θ, where θ is the angle between the magnetic field and the direction of motion, the equation becomes,

E = BLv sin θ

The maximum e.m.f is generated when the conductor moves at right angles to the field.

Calculation:

Given that, Magnetic flux density (B) = 1.1 T

Length (l) = 0.5 m

Emf induced is, E = 16.5 V

⇒ 16.5 = 1.1 × 0.5 × l × sin 90°

⇒ l = 30 m/s