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In the presence of electric field ⃗E(⃗r) and magnetic field ⃗B(⃗r), a point like positive charge q is moving antiparallel to magnetic field with velocity ⃗v. Then force acting on a charge q at a position ⃗r at time t due to both of them is

Asked in GSEB Board July 2023 · Crossed electric and magnetic fields

• (1) -q⃗E(⃗r)
• (2) q⃗E(⃗r)
• (3) -q⃗E(⃗r)+q[⃗v×⃗B(⃗r)]
• (4) q⃗E(⃗r)+q[⃗v×⃗B(⃗r)]

Step-by-step solution

Why the other options are wrong

• (1) The sign is wrong. The charge is positive, so the electric force runs along ⃗E; -q⃗E is the force on a negative charge of the same size.
• (3) Both mistakes at once: the electric term has the wrong sign, and the magnetic term is kept although it vanishes here.
• (4) The general Lorentz force, right for any moving charge. But this charge moves antiparallel to ⃗B, so ⃗v×⃗B=vB sin 180°=0 and the second term drops out.

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