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A rectangular coil of 200 turns or wire ...

A rectangular coil of 200 turns or wire `15 xx 40 cm^(2)` makes 50 r.p.s. about an axis in its plane parallel to its longer side and perpendicular to a magnetic field of intensity `0.08 Wb//m^(2)`. What are the instantaneous values of induced e.m.f. when the plane of the coil makes an angle with magnetic field of (a) `0^(@)` (b) `60^(@)` (c) `90^(@) ?`

Text Solution

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Here, `N = 200`,
`A = 15 xx 40 cm^(2) = 600 xx 10^(-4) m^(2)`,
`v = 50 r.p.s, B = 0.08 Wb//m^(2), e = ?`
`e_(0) = NAB omega = NAB (2 pi v ) = (200)`
`xx (6 xx 10^(-2)) xx 0.08 xx 2 xx (22)/(7) xx 50`
`= 301.7` volt
In the question, angle are given between the plane of the coil and magnetic field. We have to use angles which normal to plane of coil makes with the field. Therefore, from `e = e_(0) sin omega t = e_(0) sin theta`
(a) Here `theta = 90^(@) - 0^(@) = 90^(@)`.
`e = 301.7 sin 90^(@)`
`= 301.7` volt
(b) Here, `theta = 90^(@) - 60^(@) = 30^(@)`
`e = 301.7 sin 3.0^(@) = 301.7 xx (1)/(2)`
` = 150.85` volt
(c ) Here, `theta = 90^(@) - 90^(@) = 0^(@)`
`e = 301.7 sin 0^(@)`
= zero.
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