A particle having the same charge as of electron moves in a circular… | JEE Main 2019 (9 Jan, Shift 2)

Q91JEE Main 2019 · 9 JAN · SHIFT 2Medium

Moving Charge in a Magnetic Field

A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron = 1.6 $\times$ 10 $-$ 19 C)

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Answer: (d)

Straight path when $qE = qvB$ : $v = \dfrac{E}{B} = \dfrac{100}{0.5} = 200\text{ m/s}$ .
Circular path: $r = \dfrac{mv}{qB} \Rightarrow m = \dfrac{qBr}{v}$ .
$m = \dfrac{1.6 \times 10^{-19} \times 0.5 \times 0.5 \times 10^{-2}}{200} = 2.0 \times 10^{-24}\text{ kg}$
So the answer is (d) $2.0 \times 10^{-24}\text{ kg}$ .

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