A particle with charge to mass ratio, frac{q}{m} = α is shot with a speed v towards a w

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4.Moving Charges and Magnetism

medium

A particle with charge to mass ratio, $\frac{q}{m} = \alpha $ is shot with a speed $v$ towards a wall at a distance $d$ perpendicular to the wall. The minimum value of $\vec B$ that exist in this region perpendicular to the projection of velocity for the particle not to hit the wall is

$\frac{v}{{\alpha d}}$

$\frac{2v}{{\alpha d}}$

$\frac{v}{{2\alpha d}}$

$\frac{v}{{4\alpha d}}$

Solution

The situation is shown in the figure.

Let the particle projected at the point $O$, undergo deflection due to the applied magnetic field $\overrightarrow{B}$ in a direction normally inwards and let it just miss hitting the wall at $A$.

Then, $\mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}}$

For the particle not to hit the wall i.e. to just miss hitting the wall,

$r=d \Rightarrow \frac{m v}{q B}=d$

$\Rightarrow \mathrm{B}=\frac{\mathrm{mv}}{\mathrm{qd}}=\frac{\mathrm{v}}{\alpha \mathrm{d}}$

Standard 12

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medium

A particle with charge to mass ratio, $\frac{q}{m} = \alpha $ is shot with a speed $v$ towards a wall at a distance $d$ perpendicular to the wall. The minimum value of $\vec B$ that exist in this region perpendicular to the projection of velocity for the particle not to hit the wall is

Solution

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