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GATE 2026 EE – Question 16

Electromagnetic Fields · Biot-Savart law, Ampere law, Curl, Faraday law, Lorentz force · 1 mark · Multiple choice

A positive point charge with velocity $\vec v=5\,\hat x$ enters a region having electric field $\vec E=4\,\hat y$ and magnetic field $\vec B=-6\,\hat z$. Which one of the following statements is correct for the force on the charge as it enters the region?

  1. The force will be along the magnetic field but perpendicular to the electric field
  2. The force will be along the electric field but perpendicular to the magnetic field
  3. The force will be perpendicular to both electric and magnetic field
  4. The magnetic field does not exert any force on the charge

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Correct answer: (B) The force will be along the electric field but perpendicular to the magnetic field

Explanation

$\vec F=q(\vec E+\vec v\times\vec B)$. $\vec v\times\vec B=5\hat x\times(-6\hat z)=-30(\hat x\times\hat z)=-30(-\hat y)=+30\hat y$. The total is $q(4+30)\hat y=34q\,\hat y$: along the electric field ($\hat y$) and perpendicular to the magnetic field ($\hat z$).