Please help with this physics question. Thank you! The following constants can b
ID: 1522815 • Letter: P
Question
Please help with this physics question. Thank you!
The following constants can be used:
ke = 8.99×109 Nm2/C2
qe = 1.6×10–19 C
mp = 1.67×10–27 kg
me = 9.11×10–31 kg
eps0 = 8.85×10–12 C2/(Nm2)
g = 9.80 m/s2
Hints:
The physics is easy as long as you remember to set the total force on the middle charge be equal to zero.
Does the force between the charges at the ends of the rods matter? What is the distance between the middle charge and each of the other charges?
You may have to brush up on your algebra to get this problem right! Its easier to wait to the end to plug in numerical values.
Remember:
Two small beads having positive charges 3q 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 the figure, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Take q=1.24 ?C and d=70.7 cm.
Defined symbols:
d length of the rod in m
q charge of the small bead in ?C
The answer is x the position of the third bead in equilibrium in cm
Hints:
The physics is easy as long as you remember to set the total force on the middle charge be equal to zero.
Does the force between the charges at the ends of the rods matter? What is the distance between the middle charge and each of the other charges?
You may have to brush up on your algebra to get this problem right! Its easier to wait to the end to plug in numerical values.
Remember:
Range of answers: 30.0 cm to 60.0 cm
Explanation / Answer
here,
q = 1.24 * 10^-6 C
d = 0.707 m
let the distance of bead from the origin be x at equilibrium
the bead is at equilibrium at the point where the elctric feild is zero
E = k * 3 * q /x^2 - k *q /( d - x)^2
as the elctric feild is zero
0 = k * 3 * q /x^2 - k *q /( d - x)^2
0 = 3 /x^2 - 1 /( d - x)^2
3 /x^2 - 1/( 0.707 - x)^2 = 0
x = 0.45 m
x = 44.8 cm
the bead is in equilibrium at x = 44.8 cm