A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earths magnetic field 0.60 × 10⁻⁴ Wbm⁻². The instantaneous value of emf induced in the wire when its velocity is 10 ms⁻¹ is _________ × 10⁻³ V.

Solution

Physics sir · 3 steps

Wire, velocity and field are all at right angles here, so the emf is just Bvl with no sine to worry about.

1. Check the directions. The wire lies east to west and falls straight down. The horizontal component of the earth's field points south to north. These three directions are mutually perpendicular, so the full B_H and the full v count.

   e = B_H v l

2. Put in numbers. e = 0.60 × 10⁻⁴ × 10 × 5 = 30 × 10⁻⁴ V = 3 × 10⁻³ V.
3. So. The instantaneous emf is 3 × 10⁻³ V, so the blank is 3.

The common slip: 0.003. Reporting the emf in volts gives 0.003, but the blank already carries × 10⁻³ V, so the answer to enter is 3.

The idea to keep. For motional emf, first check that the rod, its velocity and the field are mutually perpendicular. If they are, e = Bvl. If not, use only the field component perpendicular to both.

Answer from the NTA final answer key. Solution by PrepWiser.