Hello there Brainliacs, try and solve the following question and earn 50 points.
Two particles A and B. each carrying a charge Q, are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the middle point of the line AB.
(a) If it is displaced through a distance x perpendicular to AB, what would be thebelectric force experienced by it.
(b) Assuming x <<d,
show that this force is proportional to x.
(c) Under whatconditions will the particle C execute simple harmonic motion if it is released after such a small displacement ?
(d)Find the time period of the oscillations if these
conditions are satisfied.
PLZ No Slamming.
Answers
Answer:
Hey mate here is your answer....
The charge q is displaced by a distance x on the perpendicular bisector of AB.
The charge q is displaced by a distance x on the perpendicular bisector of AB.As shown in the figure, the horizontal component of the force is balanced.
sinθ=xd22+x2
Total vertical component of the force, F'=2Fsinθ
F'=2×14πε0×qQd22+x2×xd22+x2⇒F'=12πε0×qQxd22+x23/2
F'=2×14πε0×qQd22+x2×xd22+x2⇒F'=12πε0×qQxd22+x23/2This is the net electric force experienced by the charge q✅✅.
(b) When x < < d:
F'=12πε0qQxd23 ∵x2<<d22⇒F'=4πε0qQxd3
(c) For the particle to execute simple harmonic motion:
F' = mw2x
F' = mw2x⇒4πε0qQxd3=m2πT2x⇒T2=mπ3ε0d3Qq⇒ T =mπ3ε0d3Qq1/2✅✅✅➡️⬅️⬅️⬅️
thanks
hope it's helpful for you...
Hola mate
Here is your answer -
The charge q is displaced by a distance x on the perpendicular bisector of AB.
The charge q is displaced by a distance x on the perpendicular bisector of AB.As shown in the figure, the horizontal component of the force is balanced.
sinθ=xd22+x2
Total vertical component of the force, F'=2Fsinθ
F'=2×14πε0×qQd22+x2×xd22+x2⇒F'=12πε0×qQxd22+x23/2
F'=2×14πε0×qQd22+x2×xd22+x2⇒F'=12πε0×qQxd22+x23/2This is the net electric force experienced by the charge q.
(b) When x < < d:
F'=12πε0qQxd23 ∵x2<<d22⇒F'=4πε0qQxd3
(c) For the particle to execute simple harmonic motion:
F' = mw2x
F' = mw2x⇒4πε0qQxd3=m2πT2x⇒T2=mπ3ε0d3Qq⇒ T =mπ3ε0d3Qq1/2