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A circular coil of radius 6 cm and 20 tu...

A circular coil of radius `6 cm` and 20 turns rotates about its vertical diameter with an angular speed of `40"rad"s^(-1)` in a uniform horizontal magnetic field of magnitude `2xx10^(-2)T`. If the coil form a closed loop of resistance `8 Omega`, then the average power loss due to joule heating is

A

`2.07xx10^(-3)W`

B

`1.23xx10^(-3)W`

C

`3.14xx10^(-3)W`

D

`1.80xx10^(-3)W`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `r=6cm =6xx10^(-2)m`,
`N=20,omega=40 "rad" s^(-1)`
`B=2xx10^(-2)T,R=8Omega`
Maximum emf induced, `epsi=NABomega`
`=N(pir^(2))Bomega`
`=20xxpixx(6xx10^(-2))^(2)xx2xx10^(-2)xx40=0.18V`
Average value of emf induced over a full cycle `epsi_(av)-0`
Mixmum, value of current in the coil,
`I=(epsi)/(R)=(0.18)/(8)=0.023A`
Average power dissipated,
`P=(epsil)/(2)=(0.18xx0.023)/(2)=2.07xx10^)-3) W`
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