1 2:24 3. ty Notes Ask Your Teach 1 polnts SerPSE 23 P013. Two small beads havin

Question

1 2:24 3. ty Notes Ask Your Teach 1 polnts SerPSE 23 P013. Two small beads having positive charges q1 = 189 and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d 1.50 m. The bead with charge q1 is at the origin. As shown in the figure below, a third small, charged bead is free to slide on the rod 91 92 (a) At what position x is the third bead in equilibrium? (b) Can the equilibrium be stable? yes, if the third bead has a posltive charge yes, if the thind bead has a negative charpe O No

Explanation / Answer

the 3rd (positive) charge Q and take its equilibrium position as x=X.

Distance from q1 to Q is X
Force on Q due to q1 = k(18q)Q/X² acting to the right (see link)

Distance from q2 to Q is 1.5-X
Force on Q due to q2 = k(q)Q/(1.5-X)² acting to the left (see link)

When Q is in equilibrium these 2 opposite direction forces must have equal magnitudes:

k(18q)Q/X² = k(q)Q/(1.5-X)²
18/X² = 1/(1.5-X)²

Square root both sides
4.24/X = 1/(1.5-X)

4.24(1.5-X) = X
6.36 - 4.24X = X
5.24X = 6.36
X = 1.21m

b) yes if the third bead has a positive charge

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