Question : A positive charge Q is fixed at a point in space. There is another charge -q which moves in a circular path of radius r around a given fixed charge. Assumed that the Electric force is the only force acting between them. Calculate the time period of revolution of charge.
Doubt by Zoha
Solution :
Here
q1=Q
q2=-q
r = r
At equilibrium
Coulomb Force between the Two charges must be equal to the Force of centripetal.
Coulomb Force between the Two charges must be equal to the Force of centripetal.
Coulomb Force = Centripetal Force
K|q1||q2|/r² = mv²/r
K|Q||-q|/r = mv²/r
KQq/r²=mv²/r
KQq/mr=v²
v²=KQq/mr
K|Q||-q|/r = mv²/r
KQq/r²=mv²/r
KQq/mr=v²
v²=KQq/mr
v=√(KQq/mr)— (1)
Also, In uniform Circular Motion
v = 2πr/T [∵Speed = Distance/Time].
√(KQq/mr) = 2πr/T
T = 2πr/[√(KQq/mr)]
T = √[4π²r³m/KQq]
T = 2πr/[√(KQq/mr)]
T = √[4π²r³m/KQq]
T = √[(4π²r³m×4πɛ₀)/Qq]
T= √[16π³r³ɛ₀m/Qq]
T= √[16π³r³ɛ₀m/Qq]
T = 4πr√[πrɛ₀m/Qq]
