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A circular coil of rauis 10cm, 500 turns...

A circular coil of rauis 10cm, 500 turns and resistance `2Omega` is placed with its plane perpendicualr to the horizontal component of the earth's magnetic field it is rotated about its vertical diameter through `180^(@)` in 0.25 S estimate the magnitude of the emf and current induced in the coil. Horizontal component of earth's magnetic field at the place is `3xx10^(-5)T.`

Text Solution

Verified by Experts

Given :
Radius, `r=10cm=0.1m`
N = 500 turns
Resistance, `R=2Omega`
`theta_(1)=0^(@),theta=180^(@)`
To find :
`dt=0.25s,e=e?,I=?`
Solution :
`B=3xx10^(-5)T`
`A=pir^(2)=3.14xx(10^(-1))^(2)`
`A=3.14xx10^(-2)m^(2)`
`e=-(N(dphi))/(dt)=(N(phi_(2)-phi_(1)))/(dt)`
`=-(MBA(costheta_(2)-costheta_(1)))/(dt)`
`e=(500xx3xx10^(-5)xx3.14xx10^(-2)(cos180^(@)-cos0^(@)))/(0.25)`
`c=3.8xx10^(-3)V`
`I=(e)/(R)=(3.8xx10^(-3))/(2)`
`I=1.9xx10^(-3)A`
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