A particle of mass 10⁻² kg and charge 5 × 10⁻⁸ C is given a horizontal velocity 10⁵ m/s in electric and magnetic fields. To maintain horizontal motion, which pairs of statements are possible? (I) B⃗ ⟂ v⃗ and E⃗ ∥ v⃗. (II) Both B⃗ and E⃗ are parallel to v⃗. (III) B⃗, E⃗ and v⃗ are mutually perpendicular. (IV) B⃗ ∥ v⃗ and E⃗ ⟂ v⃗.
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Question

A particle of mass 10⁻² kg and charge 5 × 10⁻⁸ C is given a horizontal velocity 10⁵ m/s in electric and magnetic fields. To maintain horizontal motion, which pairs of statements are possible? (I) B⃗ ⟂ v⃗ and E⃗ ∥ v⃗. (II) Both B⃗ and E⃗ are parallel to v⃗. (III) B⃗, E⃗ and v⃗ are mutually perpendicular. (IV) B⃗ ∥ v⃗ and E⃗ ⟂ v⃗.

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G1 Physics · Accepted Answer

Step 1: The question tests whether a charged particle can continue along a straight horizontal path under the ELECTROMAGNETIC force F⃗ = q(E⃗ + v⃗ × B⃗) (the textbook neglects gravity here). Step 2: For statement II, both fields are parallel to v⃗. Then v⃗ × B⃗ = 0, and qE⃗ acts along the existing line of motion; it does not bend the path. Step 3: For statement III, choose mutually perpendicular E⃗, B⃗ and v⃗ so qE⃗ exactly cancels q(v⃗ × B⃗), i.e. E = vB in magnitude. The net transverse force…