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Magnetics question

2022 · 24 Jun · Shift 1 · Q45
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Magnetics question

2022 · 24 Jun · Shift 1 · Q45

JEE MainPhysicsMagneticsMCQ+4 / −1
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.
  1. A
    Both (A) and (R) are true and (R) is the correct explanation of (A).
  2. B
    Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
  3. C
    (A) is true but (R) is false.
  4. D
    (A) is false but (R) is true.
View written solutionFree

Correct answer: A

  1. Magnetic force on a moving charge

    For a charged particle moving in a magnetic field, F⃗=q(v⃗×B⃗).\vec F = q(\vec v \times \vec B).F=q(v×B).

    Hence, the magnetic force is always perpendicular to both v⃗\vec vv and B⃗\vec BB.

  2. Check the Reason (R)

    The statement says: Moving charged particle experiences magnetic force perpendicular to its direction of motion.

    This is true, because from F⃗=q(v⃗×B⃗),\vec F = q(\vec v \times \vec B),F=q(v×B), we get F⃗⊥v⃗.\vec F \perp \vec v.F⊥v.

    So, (R) is true.

  3. Effect on speed and energy

    Work done by a force is related to the component of force along displacement. Since magnetic force is always perpendicular to velocity, it does no work: P=F⃗⋅v⃗=0.P = \vec F \cdot \vec v = 0.P=F⋅v=0.

    Therefore, the kinetic energy remains constant: K=12mv2=constant.K = \frac{1}{2}mv^2 = \text{constant}.K=21​mv2=constant.

    Since kinetic energy remains constant, the speed vvv also remains constant.

    So, (A) is true.

  4. Does (R) correctly explain (A)?

    Yes. Because the magnetic force being perpendicular to motion implies zero work done, which means no change in kinetic energy and hence no change in speed.

    Therefore, (R) is the correct explanation of (A).

  5. Evaluate the options

    • A: Both (A) and (R) are true and (R) is the correct explanation of (A). ✅
    • B: Incorrect
    • C: Incorrect
    • D: Incorrect

Final Answer: A\boxed{A}A​

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