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A rod of 10 cm length is moving perpendicular to a uniform magnetic field of intensity 5×10⁻⁴ Wb m⁻². If the acceleration of the rod is 5 m s⁻², then the rate of increase of the induced emf is _____.

Asked in GUJCET 2015 · Free conductor moving in a field

• (1) 25×10⁻⁴ V s
• (2) 2.5×10⁻⁴ V s⁻¹
• (3) 20×10⁻⁴ V s
• (4) 20×10⁻⁴ V s⁻¹

Step-by-step solution

Why the other options are wrong

• (1) Leaves out the rod's length (Ba = 5×10⁻⁴×5 = 25×10⁻⁴) and gives it the unit V s, which is the unit of magnetic flux, not of a rate of change of emf (V s⁻¹).
• (3) No single slip gives 20×10⁻⁴, and V s is the unit of magnetic flux, not of a rate of change of emf.
• (4) Right unit, wrong size: no single slip gives 20×10⁻⁴ V s⁻¹. Sanity check: Bℓ a = 5×10⁻⁴×0.1×5 = 2.5×10⁻⁴ V s⁻¹.

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