Question
Inside a solenoid of radius 0.5 m , magnetic field is changing at a rate of 50 10^ -6 ~T / s . Acceleration of an electron placed at a distance of 0.3 m from axis of solenoid will be
BITSAT
Physics
Electromagnetic Induction
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Physics Question (2024) — Solution
Options
- A. 23 10^6 ~ms ^ -2
- B. 26 10^6 ~m / s ^2
- C. 1.3 10^9 ~ms ^ -2
- D. 26 10^9 ~m / s ^2
Answer
A. 23 10^6 ~ms ^ -2
Step-by-step solution
The changing magnetic field induce an electric field which will accelerate the electron. The acceleration of electron will be a= e E m [ F=q E] To find electric field E, we will use Faraday's electromagnetic induction. emf , = -d d t (B A) where, B is the magnetic field and A is the area of cross-section. =-A d B d t =- r^2 d B d t Now, electric field, E=- emf distance =- d = r^2 d d B d t Now, acceleration, a= e m r^2 d d B d t = 1.6 10^ -19 9.1 10^ -31 22 7 aligned & (0.5)^2 (0.3) 50 10^ -6 \\ & =23 10^6 ~ms ^ -2 aligned
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