Magnetic Fields due to Electric Current — Flashcards
Maharashtra Board · Class 12 · Physics
25 flashcards for Magnetic Fields due to Electric Current (Maharashtra Board Class 12 Physics) to test yourself on key terms and facts.
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What is the Lorentz force law and what are its key implications for charged particles in magnetic fields?
Answer
The Lorentz force law states that the force on a charge q moving with velocity v⃗ in electric field E⃗ and magnetic field B⃗ is: F⃗ = q[E⃗ + (v⃗ × B⃗)]. Key implications: (1) If v⃗ ∥ B⃗, magnetic forc…
Derive the formula for the radius of curvature in cyclotron motion and state the cyclotron frequency.
Answer
For a charged particle in uniform magnetic field B⃗ ⊥ to velocity: Magnetic force provides centripetal force: qvB = mv²/R. Therefore, R = mv/qB (cyclotron radius). The cyclotron frequency is fc = qB/2…
A proton enters a magnetic field of 1.5 T with velocity 2 × 10⁶ m/s perpendicular to the field. Calculate the radius of curvature and cyclotron frequency. (mp = 1.67 × 10⁻²⁷ kg, e = 1.6 × 10⁻¹⁹ C)
Answer
Given: B = 1.5 T, v = 2 × 10⁶ m/s, q = e = 1.6 × 10⁻¹⁹ C, m = 1.67 × 10⁻²⁷ kg Radius: R = mv/qB = (1.67 × 10⁻²⁷ × 2 × 10⁶)/(1.6 × 10⁻¹⁹ × 1.5) = 0.0139 m = 1.39 cm Frequency: fc = qB/2πm = (1.6 × 10⁻¹…
What is the principle and working of a cyclotron accelerator?
Answer
Cyclotron uses crossed electric and magnetic fields to accelerate charged particles. Two semicircular 'dees' have alternating voltage. Magnetic field (⊥ to dees) causes circular motion while electric …
Describe helical motion of charged particles in magnetic fields and give its applications.
Answer
When a charged particle has velocity components both parallel (v∥) and perpendicular (v⊥) to magnetic field B⃗: v∥ is unaffected (no magnetic force), v⊥ causes circular motion. Result: helical motion …
State the formula for magnetic force on a straight current-carrying wire and derive it from the Lorentz force law.
Answer
For straight wire of length L carrying current I in magnetic field B⃗: F⃗ = IL⃗ × B⃗. Derivation: Charge flowing in time t = It = IL/vd. Force on this charge: F⃗ = q(v⃗d × B⃗) = (IL/vd)(vd × B⃗) = IL⃗…
Why is the net force on a closed current loop zero in a uniform magnetic field?
Answer
For a closed loop in uniform magnetic field B⃗: F⃗ = I∮dl⃗ × B⃗ = I(∮dl⃗) × B⃗. Since ∮dl⃗ = 0 for any closed path (vector sum of displacement around closed loop is zero), the net force F⃗ = 0. Howeve…
Derive the expression for torque on a rectangular current loop in a magnetic field.
Answer
For rectangular loop (length l₁, width l₂) at angle θ to field B⃗: Forces on sides perpendicular to B⃗ are F = Il₁B (equal and opposite), creating torque. Moment arm = ½l₂sinθ. Total torque: τ = 2 × I…
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