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A thin ring of 10 cm radius carries a un...

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of `40pi "rad s"^(-1)` about its axis, perpendicular to its plane. If the magnetic field at its centre is `3.8xx10^(-9)T`, then the charge carried by the ring is close to `(mu_(0)=4pi xx10^(-7)N//A^(2))`

A

`3xx10^(-5)C`

B

`7xx10^(-6)C`

C

`4xx10^(-5)C`

D

`2xx10^(-6)C`

Text Solution

Verified by Experts

The correct Answer is:
A

`omega=(2pi)/(T)" "B=(mu_(0))/(4pi)(I)/(r)phi`
`I=(q)/(T)" "B=(mu_(0))/(4pi)(I)/(r).2pi`
`I=(q)/(2pi//omega)" "B=(mu_(0))/(4pi).2pi(I)/(r)`
`I=(qomega)/(2pi)" "3.8xx10^(-9)=10^(-7)xx2pixx(qomega)/(2pir)`
`" "3.8xx10^(-9)=10^(-7)xxqxx(40pi)/(10xx10^(-2))`
`q=(3.8xx10^(-9)xx10xx10^(-2))/(40pi xx10^(-7))`
`q=(3.8xx10^(-10)xx10^(7))/(40xx(22)/(7))`
`q=(3.8xx10^(-3)xx7)/(40xx22)`
`q=0.030xx10^(-3)C`
`q=3xx10^(-5)C`
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