Motional Emf
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?
Select the correct option:
Solution
1.6 V
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 ε=Blv, arising because the magnetic force on free electrons in the rod separates charge until an electrostatic field balances it. Substituting the given values: ε=0.8×0.5×4=1.6 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 T⋅m⋅m/s=V, since 1 T=1 V\cdotps/m2, confirming the dimensional consistency of the answer, and a value of a few volts is physically reasonable for these modest laboratory quantities.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic induction and alternating currents
- Topic
- motional emf
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1.6 V
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 ε=Blv, arising because the magnetic force on free electrons in the rod separates charge until an electrostatic field balances it. Substituting the given values: ε=0.8×0.5×4=1.6 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 T⋅m⋅m/s=V, since 1 T=1 V\cdotps/m2, confirming the dimensional consistency of the answer, and a value of a few volts is physically reasonable for these modest laboratory quantities.
This easy difficulty physics question is from the chapter electromagnetic induction and alternating currents, covering the topic of motional emf. It appeared in the 2025 exam.
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