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JEE Main 2014 (12 Apr, Shift 1) · Moving Charge in a Magnetic Field

Moving Charge in a Magnetic Field question from JEE Main 2014 (12 Apr, Shift 1)

Q100JEE Main 2014 · 12 APR · SHIFT 1Difficult

Moving Charge in a Magnetic Field

A positive charge 'q' of mass 'm' is moving along the + x axis. We wish to apply a uniform magnetic field B for time Δ\Deltat so that the charge reverses its direction crossing the y axis at a distance d. Then:

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Answer: (c)

  1. To reverse direction, the charge makes a semicircle whose diameter is dd, so r=d2r = \dfrac{d}{2}.
  2. r=mvqB=d2⇒B=2mvqdr = \dfrac{mv}{qB} = \dfrac{d}{2} \Rightarrow B = \dfrac{2mv}{qd}
  3. Time for a semicircle: Δt=πrv=πd2v\Delta t = \dfrac{\pi r}{v} = \dfrac{\pi d}{2v}
  4. So the answer is (c).
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