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Derivation of the expression AT) = Kb X m:- |
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Answer» ong>Answer: from silk threads of length ℓ and carry similar charges +q and +q. (a) Prove that when the system is in equilibrium, separation between the balls is x=( 2πε 0
mg q 2 ℓ
) 1/3 , assuming the angle made by the threads with the vertical LINE passing through the point of suspension is small. (b) Specify the rate (dq/dt) with which the charge from each sphere leaks off if their velocity of approach varies as V= x
a
, where a is a constant. Share Study later ANSWER (a) Force of electrostatic REPULSION: F= 4πε 0
x 2
q 2
For equilibrium of each sphere: Tcosθ=mg Tsinθ=F= 4πε 0
x 2
q 2
⟹ mg F
=tanθ ⟹= 4πε 0
x 2 (mg) q 2
=tanθ≈sinθ= 2ℓ x
[∵θ→0] ⟹x=( 2πε 0
mg q 2 ℓ
) 1/3 ...(i) (b) From equation (i) q 2 = ℓ 2πε 0
mgx 3
Differentiating both sides with respect to time: 2q dt dq
= ℓ 2πε 0
mg
.3x 2
dt dx
Now, dt dx
=velocity of approach =v= x
a
( ℓ 2πε 0
mg
) 1/2 .x 3/2
dt dq
= ℓ 3πε 0
mg
x 2 ( x
a
) USING equation (i) ⟹ dt dq
= 2 3
a ℓ 2πε 0
mg
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