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An electron (mass 9 × 10⁻³¹ kg, charge 1.6 × 10⁻¹⁹ C) moves at 3 × 10⁷ m s⁻¹ perpendicular to a field of 6 × 10⁻⁴ T. The radius of its circular path is approximately:
A2.8 cm
B28 cm
C56 cm
D14 cm
Answer & Solution
Correct answer: B. 28 cm
1. Radius of circular motion: $r = \dfrac{mv}{qB}$.
2. Numerator: $mv = 9\times10^{-31} \times 3\times10^{7} = 2.7\times10^{-23}$.
3. Denominator: $qB = 1.6\times10^{-19} \times 6\times10^{-4} = 9.6\times10^{-23}$.
4. So $r = \dfrac{2.7\times10^{-23}}{9.6\times10^{-23}} = 0.28$ m.
5. That is $r = 28$ cm.
_Source: NCERT Class 12 Physics Ch 4 "Moving Charges and Magnetism", p.139_
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