JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Magnetic Effects of Current

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In an experiment, electrons are accelerated, from rest, by applying, a voltage of 500 V . Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron

= 1.6 \times 1 0^{- 19} C

Mass of the electron

= 9.1 \times 1 0^{- 31} kg

]

(A) $7.5 \times 1 0^{- 3} m$
(B) $7.5 \times 1 0^{- 2} m$
(C)7.5 m
(D) $7.5 \times 1 0^{- 4} m$ ✓ Correct

Answer: (D)

Solution

The accelerating voltage gives each electron kinetic energy

e V

, so its momentum is

p = 2 m e V

. In the field the magnetic force supplies the centripetal force, and the radius is

R = \frac{p}{e B} = \frac{2 m e V}{e B}

. Substituting

m = 9.1 \times 1 0^{- 31} kg

V = 500 V

e = 1.6 \times 1 0^{- 19} C

and

B = 0.1 T

R = \frac{2 \times 9.1 \times 1 0 ^{- 31} \times 1.6 \times 1 0 ^{- 19} \times 500}{1.6 \times 1 0 ^{- 19} \times 0.1} \approx 7.5 \times 1 0^{- 4} m

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Magnetic Effects of Current

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