First slide

Force on a charged particle moving in a magnetic field

Question

An electron is projected with a velocity v₀ in a uniform electric field E perpendicular to the field. Again it is projected with velocity v₀ perpendicular to a uniform magnetic field. If r₁ and r₂ are initial radii of curvature just after entering in the electric field and magnetic field respectively, then the ratio r₁/r₂ is

Difficult

A

$\frac{B}{E}$
B

$\frac{{Bv}_{0}}{E}$
C

$\frac{{Ev}_{0}}{B}$
D

$\frac{E}{B}$

Solution

$\begin{array}{rcl} \frac{{mv}_{0}^{2}}{r_{1}} & = & qE \\ \Rightarrow & r_{1} = \frac{{mv}_{0}^{2}}{qE} - - - - (1) \\ \frac{{mv}_{0}^{2}}{r_{2}} & = & {qv}_{0} B \\ r_{2} & = & \frac{{mv}_{0}}{qB} - - - - (2) \\ ∴ \frac{r_{1}}{r_{2}} & = & \frac{{Bv}_{0}}{E} \end{array}$

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