# (a) Obtain the conditions under which an electron does not suffer any deflection while passing through a magnetic field.(b) Two protons P and Q moving with the same speed pass through the       magnetic fields $\vec{B_{1}}$ and $\vec{B_{2}}$ respectively, at right angles to the field       directions. If $\left | \vec{B_{2}} \right |> \left | \vec{B_{1}} \right |$, which of the two protons will describe the       circular path of smaller radius? Explain.

(a) An electron does not suffer any deflection while passing through a magnetic field when it is parallel or anti-parallel to the magnetic field.

(b) The radius of the circular path

$R=\frac{mv}{qB}$

$\frac{R_{1}}{R_{2}}=\frac{B_{2}}{B_{1}}$

Or,

$R\propto \frac{1}{B}$                [$\because$ m,v and q are constant or same ]

Thus as,

$B_{1}< B_{2}$

Hence,

$R_{2}< R_{1}$

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