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A charged particle is moving with velocity ⃗v in a uniform magnetic field ⃗B. The magnetic force acting on it will be maximum when ______.

Asked in GSEB Board July 2017 · Lorentz force and work done

• (1) ⃗v and ⃗B are in the same direction
• (2) ⃗v and ⃗B are in opposite directions
• (3) ⃗v and ⃗B are mutually perpendicular
• (4) ⃗v and ⃗B make an angle of 45° with each other

Step-by-step solution

Why the other options are wrong

• (1) With θ=0, sin θ=0 and F=qvB sin θ vanishes: a charge moving along the field lines feels no magnetic force at all.
• (2) With θ=180°, sin θ=0 again, so the force is zero here too — the smallest it can be, not the largest.
• (4) At 45°, sin θ=1/(√2)≈0.71, so the force is only about 71% of the largest value these numbers allow.

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