Question

Problem 2. m, q An infinite insulating plane has a uniform surface charge density σ-528 nC/m2. A point charge q- 465 nC of mass m 1.14 10-8 kg is released at a distance of 50 cm from the plane. The charge is initially moving toward the plane with a speed of 24.0m/s. What is the closest distance to the plane the charge reaches? (Ignore gravity in this problem.)

Answer 1

Here, we know that, electric field due to infinite sheet of charge is given by. E = sigma/2 epsilon and F = qE F = q sigma/2 epsilon_0 Using work energy theorem Work done = charge in K.E. F middot d = 1/2 mv^2 - 1/2 mu^2 v = 0 d = -1/2 mv^2 times 2 epsilon_0/q epsilon d = -1.14 times 10^-8 times (24.0)^2 times 8.85 times 10^12/-4.65 times 10^-9 times 52.8 times 10^-9 d = 23.66 cm rightwardsdoublearrow The closest distance is S = D - d S = 50 - 23.66 S = 26.34 cm.