BITSAT 2024 Shift 1 Paper

The changing magnetic field induces an electric field, which accelerates the electron.
To determine the acceleration of the electron, we use the formula:
a=‌

eE

m

where F=qE.
To calculate the electric field E, we apply Faraday's law of electromagnetic induction:
ε=−‌

dΦ

dt

=−B⋅A
Here, B is the magnetic field, and A is the cross-sectional area. Therefore, the electromotive force (emf) is:
ε=−A⋅‌

dB

dt

=−πr2⋅‌

dB

dt

The electric field E is then given by:
‌E=−‌

ε

‌ distance ‌

=−‌

ε

d

‌E=‌

πr2

d

⋅‌

dB

dt

Finally, the acceleration a is:
a=‌

e

m

⋅‌

πr2

d

⋅‌

dB

dt

Substituting the given values:
a‌=‌

1.6×10−19

9.1×10−31

×‌

22

7

×‌

(0.5)2

0.3

×50×10−6
‌=23×106ms−2