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Question
Obtain an expression for magnetic induction of a toroid of ‘N’ turns about an axis passing through its centre and perpendicular to its plane.
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Solution
The toroid is a solenoid bent into the shape of a hollow doughnut.
According to Ampere's circuital law.
`phivecB.vec(dL) = mu_0I`
Here current 'I' flow through the ring as many times as there are the N no. of turns.
∴ `phivecB.vec(dL) = mu_0NI` ......(1)
Now, B and dL are in the same direction.
∴ `phivecB.vec(dL) = BphidL`
∴ `phivecB.vec(dL) = B.(2pir)` .....(2)
From (1) and (2),
`mu_0NI = B.(2pir)`
∴ B = `(mu_0NI)/(2pir)`
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