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Magnetic Field due to a Current — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMagnetic Field due to a Current2 Marks
Question
A tightly-wound, long solenoid has n turns per unit length, a radius r and carries a current i. A particle having charge q and mass m is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid ?
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Answer


No. of turns per unit length = n,
radius of circle $= \frac{\text{r}}{2},$
current in the solenoid = i,
Charge of Particle = q,
mass of particle = m
$\therefore\text{B}=\mu_0\text{ni}$
Again $\frac{\text{mV}^2}{\text{r}}=\text{qVB}\Rightarrow\text{V}=\frac{\text{qBr}}{\text{m}}=\frac{\text{q}\mu_0\text{nir}}{2\text{m}}=\frac{\mu_0\text{ni}\ \text{qr}}{2\text{m}}$

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