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What is Toroid? Calculate the magnetic field at a point Open space exterior to the toroid |
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Answer» Solution :A slolenoid is bent in a way that both their ends are joined together to form a closed ring shape, is called as toroid . The magnetic FIELD has constant magnitude inside the toroid whereas in the interior region ( say , at POINT P ) and exteriorrigion ( say , at point Q ) , the magnetic field is zero. Inside the toroid : Let us calculate the magnetic field `B_(S) ` at point S by constructing an Amperian loop 2 of radius `r_(2)` around the point S as SHOWN in Figure. The length of the loop is`L_(2) = 2 pi r_(2)` Ampere's circuital law for the loop 2 is `underset("loop2")oint vecB_(s) . vec(dl) =mu_(0)I_("enclosed")` Let I be the current passing through the toroid and N be the NUMBER of turns of the toroid, then ` I_("enclosed") = NI ` and `underset("loop2")oint vecB_(s) . vec(dl) =underset("loop2")ointB dl cos theta = B 2 pi r_(2)` `underset("loop2")ointvecB_(s) . vec(dl) = mu_(0) NI ` ` B_(s) = mu_(0) (NI)/(2 pi r_(2))` The number of turns per unitlength is `n = N/(2 pi r_(2))` , then the magnetic field at pointS is ` B_(s) = mu_(0) n I` |
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