Question

Suppose we had a large, positively charged plate in an upright (vertical) position and a point charge with positive charge +Q. In lecture, you saw that a large charged plate gives rise to an electric field which is constant in space: we will call this electric field Eplate. Let us suppose also that we had a s bl with positive charge +q and mass m. The situation is depicted in Figure 1. +q,m +Q Figure 1 The objective of this problem is to find the location of the ball with charge +q and mass n such that it remains in place, even with electrical and gravitational forces acting Hint: This location is unique Part a Draw a free body diagran for the charged bal and clearly label the forces acting on the ball.

Answer 1

a) OP = squareroot x^2 + y^2 cos theta = P/H = y/squareroot x^2 + y^2 sin theta = x/squareroot x^2 + y^2 b) From FBD, Resolving forces in X and Y Direction. F_p = F_Q cos theta equation (1) and F_Q sin theta = Mg equation (2) [F_p = q E_plote F_Q = kqQ/(OP)^2 = kqQ/x^2 + y^2] c) Distance between point charge and the plate does not matter as Electric field due to large plate is constant in its vicinity and does not depend on distance. D) x = squareroot kQ/E [1 + (mg/qE)^2]^3/2 = squareroot (8.99 times 10^9) (3.50 times 10^-3)/7 times 10^4 [1 + (0.01 times 9.81/(3 times 10^-6) (7 times 10^4))^2]^-3/2 = squareroot (10.91643 times 10^2) (1.2182)^-3/2 x = 28.49 x almostequalto 28 m Round to two Significant figures y = squareroot kQq/mg [1 + (qE/mg)^2]^-3/2 y = squareroot (8.99 times 10^9) (8.50 times 10^-3) (3 times 10^-6)/(0.010 times 9.81) [1 + {3 times