JEE Mains · Physics · STD 12 - 4. Moving charges and magnetism
A positive charge \('q'\) of mass \('m'\) is moving along the \(+ x\) axis. We wish to apply a uniform magnetic field \(B\) for time \(\Delta t\) so that the charge reverses its direction crossing the \(y\) axis at a distance \(d.\) Then
- A \(B\, = \,\frac{{mv}}{{qd}}\) and \(\Delta t\, = \,\frac{{\pi d}}{v}\)
- B \(B\, = \,\frac{{mv}}{{2qd}}\) and \(\Delta t\, = \,\frac{{\pi d}}{2v}\)
- C \(B\, = \,\frac{{2mv}}{{qd}}\) and \(\Delta t\, = \,\frac{{\pi d}}{2v}\)
- D \(B\, = \,\frac{{2mv}}{{qd}}\) and \(\Delta t\, = \,\frac{{\pi d}}{v}\)
Answer & Solution
Correct Answer
(C) \(B\, = \,\frac{{2mv}}{{qd}}\) and \(\Delta t\, = \,\frac{{\pi d}}{2v}\)
Step-by-step Solution
Detailed explanation
The applied magnetic field provides the required centripetal force to the charge particle, so it can move in circular path of radius \(\frac{d}{2}\) \(\therefore \mathrm{Bqv}=\frac{\mathrm{mv}^{2}}{\mathrm{d} / 2}\) or, \(B = \frac{{2{\text{mv}}}}{{{\text{qd}}}}\) Time interval…
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