Question

+ Q1. Two small beads having positive charges 39 and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. As shown in figure, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium? Q2. A small, 2.00-g plastic ball is suspended by a 20.0-cm-long string in a uniform electric field as shown in figure. If the ball is in equilibrium when the string makes a 15.0° angle with the vertical, what is the net charge on the ball? E.1.000NC 200 cm 2005 Q3. A thin rod of length 1 and uniform charge per unit length 1 lies along the x axis, as shown in figure. (a) Show that the electric field at P, a distance y from the rod along its perpendicular bisector, has no x-component and is given by E = 2kAsino,/y. (b) What If? Using your result to part (a), show that the field of a rod of infinite length is E = 2k1/y Q4. A rod 14.0 cm long is uniformly charged and has a total charge of 22.04C. Determine the magnitude and direction of the electric field along the axis of the rod at a point 36.0 cm from its center.

Answer 1

1) Let the small bead be placed at a distance x from +3q and in between both the charges

the third charge will be in equilibrium if the net force on it zero

so Force on third bead by +3q = force on third bead by +q

kQ*3q / x^2 = k*Qq / (d - x)^2

3(x^2 + d^2 - 2xd) = x^2

2x^2 - 6xd + 3d^2

x = +6d - sqrt( (6d)^2 - 4*2*3d^2)) / 2*2

= 0.64 d

so the bead will be positioned at 0.64d from the +3q charge