Magnetic Effects & Magnetism

JEE Main level, single correct, medium

167 of 276

Question 167 of 276

A positive charge ' q\mathrm{q} ' of mass ' m\mathrm{m} ' is moving along the +x+x axis. We wish to apply a uniform magnetic field B for time Δt\Delta t so that the charge reverses its direction crossing the y\mathrm{y} axis at a distance d\mathrm{d}. Then:

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Answer: (C) B=2mvqd\mathrm{B}=\frac{2 \mathrm{mv}}{\mathrm{qd}} and Δt=πd2v\Delta \mathrm{t}=\frac{\pi \mathrm{d}}{2 \mathrm{v}}

The applied magnetic field provides the required centripetal force to the charge particle, so it can move in circular path of radius d2\frac{\mathrm{d}}{2}
∴Bqv=m2d/2\therefore \quad B q v=\frac{m^2}{d / 2}
or, B=2mvqd\quad B=\frac{2 \mathrm{mv}}{\mathrm{qd}}
Time interval for which a uniform magnetic field is applied
Δt=π⋅d2v\Delta \mathrm{t}=\frac{\pi \cdot \frac{\mathrm{d}}{2}}{\mathrm{v}}
(particle reverses its direction after time Δt\Delta \mathrm{t} by covering semi circle).
Δt=πd2v\Delta \mathrm{t}=\frac{\pi \mathrm{d}}{2 \mathrm{v}}

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