Motional Emf

Question

A straight conducting rod of length 0.5 m slides at a constant speed of 4 m/s along frictionless rails in a uniform magnetic field of 0.3 T directed perpendicular to the plane of motion. What EMF appears across the ends of the rod?

RankGuru · Accepted Answer

Motional EMF arises because the free charges inside a conductor moving through a magnetic field experience a magnetic force $q\vec{v}\times\vec{B}$ that drives them along the rod until an electrostatic field balances it, establishing a steady potential difference. When the rod, its velocity, and the field are mutually perpendicular, the induced EMF takes the simple form $\varepsilon = BvL$. Inserting $B = 0.3$ T, $v = 4$ m/s and $L = 0.5$ m yields $\varepsilon = 0.3 \times 4 \times 0.5 = 0.6$ V. The option 0.3 V wrongly omits the length factor. The option 1.2 V doubles the result by mistakenly using twice the rod length. The option 0.15 V halves the speed contribution. This is exactly the rail-and-rod arrangement treated in NCERT to introduce motional EMF as an alternative route to Faraday's law. A unit and magnitude check confirms T·(m/s)·m gives volts, and the small value is consistent with a short rod moving slowly in a modest field.

Motional Emf

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