The electrostatic force (F₁⃗) and magnetic force (F⃗₂) acting on a charge q moving with velocity v can be written :

Solution

Physics sir · 4 steps

Electric force ignores velocity; magnetic force is qv⃗ × B⃗, with v written first.

1. Electric force. The electric field pushes on a charge whether it moves or not, so F⃗₁ = qE⃗. Velocity does not appear, and the force is along E⃗ for a positive charge.
2. Magnetic force. A magnetic field acts only on a moving charge, and the force is perpendicular to both v⃗ and B⃗. That calls for a cross product, with v⃗ written first.

   F⃗₂ = q(v⃗ × B⃗)

3. Order matters. A cross product changes sign when you swap its factors: B⃗ × v⃗ = -(v⃗ × B⃗). So q(B⃗ × v⃗) points the opposite way to the real force.
4. So. Only (c) has F⃗₁ = qE⃗ together with F⃗₂ = q(v⃗ × B⃗).

The idea to keep. Lorentz force: F⃗ = qE⃗ + q(v⃗ × B⃗). The magnetic part is a cross product with v⃗ first. Swapping the order flips the direction.

Answer from the NTA final answer key. Solution by PrepWiser.