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Physics · Moving Charges and Magnetic Field

NEET (UG) 2025 — Question 3

An electron (mass 9×10−31 kg9 \times 10^{-31} \, \mathrm{kg} and charge 1.6×10−19 C1.6 \times 10^{-19} \, \mathrm{C}) moving with speed c/100c/100 (cc = speed of light) is injected into a magnetic field B⃗\vec{B} of magnitude 9×10−4 T9 \times 10^{-4} \, \mathrm{T} perpendicular to its direction of motion. We wish to apply a uniform electric field E⃗\vec{E} together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c=3×108 m s−1c = 3 \times 10^8 \, \mathrm{m\,s}^{-1})

  1. Option A:

    E⃗\vec{E} is perpendicular to B⃗\vec{B} and its magnitude is 27×104 V m−127 \times 10^4 \, \mathrm{V\,m}^{-1}

  2. Option B:

    E⃗\vec{E} is perpendicular to B⃗\vec{B} and its magnitude is 27×102 V m−127 \times 10^2 \, \mathrm{V\,m}^{-1}

    Correct
  3. Option C:

    E⃗\vec{E} is parallel to B⃗\vec{B} and its magnitude is 27×102 V m−127 \times 10^2 \, \mathrm{V\,m}^{-1}

  4. Option D:

    E⃗\vec{E} is parallel to B⃗\vec{B} and its magnitude is 27×104 V m−127 \times 10^4 \, \mathrm{V\,m}^{-1}

Answer: B

Step-by-step solution

For no deflection, the electric force must balance the magnetic force: qE=qvBqE = qvB. Thus E=vBE = vB. Given v=c/100=(3×108)/100=3×106 m/sv = c/100 = (3 \times 10^8)/100 = 3 \times 10^6 \, \mathrm{m/s}. Given B=9×10−4 TB = 9 \times 10^{-4} \, \mathrm{T}. E=(3×106)(9×10−4)=27×102=2700 V/mE = (3 \times 10^6)(9 \times 10^{-4}) = 27 \times 10^2 = 2700 \, \mathrm{V/m}. The electric field must be perpendicular to both the magnetic field and the velocity to cancel the magnetic force. Hence E⃗\vec{E} is perpendicular to B⃗\vec{B}. Therefore, option B is correct.

Answer key and solution verified before publishing.

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Exam
NEET (UG) 2025
Paper
2025 paper
Subject
Physics
Chapter
Moving Charges and Magnetic Field
Topic
Motion of Charged Particles in Combined Electric and Magnetic Fields

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An electron (mass 9 × 10 -31 \, kg and charge 1.6 × 10 -19 \, C )… | NEET (UG) 2025 PYQ with Solution · DhiX AI