Question

A positive charge of 5.30 μC is fixed in place. From a distance of 3.50 cm a particle of mass 5.10 g and charge +3.20 μC is fired with an initial speed of 62.0 m/s directly toward the fixed charge. How close to the fixed charge does the particle get before it comes to rest and starts traveling away?

Answer 1

Here,

let the closest distance is x

positive charge , q1 = 5.1 uC

initial distance , d = 3.6 cm = 0.036 m

mass , m = 6.8 gm = 0.0068 Kg

initial speed , u = 76 m/s

Using conservation of energy

0.5 * m * v^2 = - k q1 *q2/d + k * q1 * q2/x

0.5 * 0.0051 * 62^2 = 9*10^9 * 5.3*10^-6 * 3.5 *10^-6 * (- 1/.032 + 1/x)

solving for x

x = 0.0111156 m

x = 11.12 mm

the minimum distance will be 11.12 mm