Motional Emf

Question

A conducting rod of length 0.5 m slides along frictionless parallel rails at a constant speed of 4 m/s inside a uniform magnetic field of 0.8 T directed perpendicular to the plane of the rails. What emf is generated across the rod?

RankGuru · Accepted Answer

From NCERT Class 12, Chapter 6 (Electromagnetic Induction), a conductor of length $l$ moving with velocity $v$ perpendicular to a magnetic field $B$ develops a motional emf given by $\varepsilon = Blv$, arising because the magnetic force on free electrons in the rod separates charge until an electrostatic field balances it. Substituting the given values: $\varepsilon = 0.8 	imes 0.5 	imes 4 = 1.6\ 	ext{V}$. The option 0.4 V wrongly divides rather than multiplies one of the factors. The option 3.2 V doubles the length or velocity incorrectly. The option 2.0 V results from misusing 5 m/s or an arithmetic slip. As a sanity check, the units combine as $	ext{T} \cdot 	ext{m} \cdot 	ext{m/s} = 	ext{V}$, since $1\ 	ext{T} = 1\ 	ext{V·s/m}^2$, confirming the dimensional consistency of the answer, and a value of a few volts is physically reasonable for these modest laboratory quantities.

Motional Emf

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