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The electrostatic force (F⃗₁) and magnetic force (F⃗₂) acting on a charge q moving with velocity v⃗ can be written

Asked in JEE Main 5th April 2nd Shift 2024 · Lorentz force and work done

(1) F⃗₁ = qB⃗, F⃗₂ = q(B⃗ × v⃗)
(2) F⃗₁ = qE⃗, F⃗₂ = q(B⃗ × v⃗)
(3) F⃗₁ = qE⃗, F⃗₂ = q(v⃗ × B⃗)
(4) F⃗₁ = qv⃗ · E⃗, F⃗₂ = q(B⃗ · v⃗)

Answer: (3) F⃗₁ = qE⃗, F⃗₂ = q(v⃗ × B⃗)

Step-by-step solution

Electric force: F⃗₁ = qE⃗.

Magnetic force: F⃗₂ = q(v⃗ × B⃗), order v⃗ then B⃗.

Why the other options are wrong

(1) Uses the magnetic field in the electric force and reverses the cross product order.
(2) Reverses the cross product order, which flips the direction of the magnetic force.
(4) Uses dot products, which give scalars, not forces.

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