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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

An infinitely long straight conductor carries a current of 5 A5 \text{ A}. An electron is moving with a speed of 105 m/s10^5 \text{ m/s} parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm20 \text{ cm} at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

A

4π×10−20 N4\pi \times 10^{-20} \text{ N}

B

8×10−20 N8 \times 10^{-20} \text{ N}

C

4×10−20 N4 \times 10^{-20} \text{ N}

D

8π×10−20 N8\pi \times 10^{-20} \text{ N}

Step-by-Step Solution

  1. Calculate Magnetic Field (BB): The magnitude of the magnetic field produced by an infinitely long straight conductor at a perpendicular distance rr is given by: B=μ0I2πrB = \frac{\mu_0 I}{2\pi r} Given I=5 AI = 5 \text{ A}, r=20 cm=0.2 mr = 20 \text{ cm} = 0.2 \text{ m}, and μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}. B=4π×10−7×52π×0.2=2×10−7×50.2=10−60.2=5×10−6 TB = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0.2} = \frac{2 \times 10^{-7} \times 5}{0.2} = \frac{10^{-6}}{0.2} = 5 \times 10^{-6} \text{ T}
  2. Determine Angle (θ\theta): The magnetic field lines around a straight wire are concentric circles. Since the electron moves parallel to the wire, its velocity vector (vv) is perpendicular to the magnetic field vector (BB) at that point (tangent to the circle). Thus, θ=90∘\theta = 90^\circ.
  3. Calculate Magnetic Force (FF): The force on a moving charge is given by the Lorentz force law: F=qvBsin⁡θF = qvB \sin\theta. Given electron charge q=1.6×10−19 Cq = 1.6 \times 10^{-19} \text{ C} and speed v=105 m/sv = 10^5 \text{ m/s}. F=(1.6×10−19)×(105)×(5×10−6)×sin⁡(90∘)F = (1.6 \times 10^{-19}) \times (10^5) \times (5 \times 10^{-6}) \times \sin(90^\circ) F=1.6×5×10−19+5−6F = 1.6 \times 5 \times 10^{-19 + 5 - 6} F=8.0×10−20 NF = 8.0 \times 10^{-20} \text{ N}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOVING CHARGES AND MAGNETISMinfinitelystraightconductorcarriescurrent

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