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Magnetics question

2019 · 9 Jan · Shift 2 · Q67
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Magnetics question

2019 · 9 Jan · Shift 2 · Q67

JEE MainPhysicsMagneticsMCQ+4 / −1
A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 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 −-− 19C)
  1. A
    9.1 ×\times× 10 −-− 31 kg
  2. B
    1.6 ×\times× 10 −-− 27 kg
  3. C
    1.6 ×\times× 10 −-− 19 kg
  4. D
    2.0 ×\times× 10 −-− 24 kg
View written solutionFree

Correct answer: D

  1. Given data
  • Charge magnitude of particle: q=1.6×10−19 Cq = 1.6 \times 10^{-19}\,\text{C}q=1.6×10−19C
  • Magnetic field: B=0.5 TB = 0.5\,\text{T}B=0.5T
  • Radius of circular path: r=0.5 cm=0.5×10−2 m=5×10−3 mr = 0.5\,\text{cm} = 0.5 \times 10^{-2}\,\text{m} = 5 \times 10^{-3}\,\text{m}r=0.5cm=0.5×10−2m=5×10−3m
  • Electric field: E=100 V/mE = 100\,\text{V/m}E=100V/m

The particle has the same charge as an electron, so its charge magnitude is eee.

  1. Use the condition for straight-line motion in crossed electric and magnetic fields

When the electric field makes the particle move in a straight path, the electric force balances the magnetic force:

qE=qvBqE = qvBqE=qvB

So,

v=EB=1000.5=200 m/sv = \frac{E}{B} = \frac{100}{0.5} = 200\,\text{m/s}v=BE​=0.5100​=200m/s

  1. Use circular motion under magnetic field alone

For motion in a circular path under magnetic field,

qvB=mv2rqvB = \frac{mv^2}{r}qvB=rmv2​

So,

m=qBrvm = \frac{qBr}{v}m=vqBr​

Substitute the values:

m=(1.6×10−19)(0.5)(5×10−3)200m = \frac{(1.6 \times 10^{-19})(0.5)(5 \times 10^{-3})}{200}m=200(1.6×10−19)(0.5)(5×10−3)​

Now simplify step by step:

0.5×5×10−3=2.5×10−30.5 \times 5 \times 10^{-3} = 2.5 \times 10^{-3}0.5×5×10−3=2.5×10−3

1.6×10−19×2.5×10−3=4.0×10−221.6 \times 10^{-19} \times 2.5 \times 10^{-3} = 4.0 \times 10^{-22}1.6×10−19×2.5×10−3=4.0×10−22

m=4.0×10−22200=2.0×10−24 kgm = \frac{4.0 \times 10^{-22}}{200} = 2.0 \times 10^{-24}\,\text{kg}m=2004.0×10−22​=2.0×10−24kg

  1. Match with options

2.0×10−24 kg2.0 \times 10^{-24}\,\text{kg}2.0×10−24kg

This corresponds to Option D.

  1. Comparison with stored answer

Stored correct answer: D

My derived answer: D

So they agree.

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