First slide

Motion of charged particle in uniform electric field

Question

There exists a uniform electric field E in horizontal direction. A particle having mass m and charge q is projected with a velocity u in upward direction in uniform gravitational field g as shown in the figure. The radius of curvature of path of particle at the highest point is

Moderate

A

$\frac{q^{2} E^{2} u^{2}}{m^{2} g^{2}}$
B

$\frac{q^{2} E^{2} u^{2}}{m^{2} g^{3}}$
C

$\frac{q^{2} E^{2} u^{2}}{m g}$
D

None of these

Solution

After time t the particle will reach the highest point of its trajectory where its horizontal component of velocity V $V_{h} = \frac{q E}{m} (\frac{u}{g}) T h e r e f o r e r a d i u s o f c u r v a t u r e ρ i s g i v e n b y {(V_{h})}^{2} / ρ = g \Rightarrow ρ = \frac{q^{2} E^{2} u^{2}}{m^{2} g^{3}}$

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