Read before you solve · 3 min

Read Motional EMF: Integrate the Field Along the Rod

This short read prepares one exact NSEP pattern: motional emf in a nonuniform wire field. Identify the physical condition before calculating.

NSEP · Electromagnetic Induction · 1 linked question · 100% coverage

Know this first

Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.

Distance · Length of the path travelledDisplacement · Straight-line change in positionResultant force · Net force including direction

Study deeper: NCERT Physics · Electromagnetic Induction

Start with the physical model

Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.

The magnetic field of the long wire at distance x is B(x)=µ0I/(2πx).

The rod moves parallel to the wire, so the motional emf

ε = ∫vB dl = (µ0Iv/2\pi )∫2l 3l dx/x = (µ0Iv/2\pi ) \ln (3/2)

This is the expression in option D.

Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.

OlympIQ trap

Using B at one end times the full length misses the logarithm from the long wire's 1/r field.

100% coverage across the linked question.