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A thin conductingstrip of width h = 2.0 cm is tightlywoudnd in the spaheof a verylong coil with cross-secitonradius R = 2.5 cmto make a single-layerstraightsolenoid. A directcurretnt I = 5.0A flows throughthe strip. Find the magneticinductininsideand outsidethe solenoidas a funcitionof the distanance r from its axis. |
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Answer» Solution :If the strip is tightly wound it must have a picvh of `h`. This means that the current will FLOW obiliquenlty, party along `hat(e)_(varphi)` and partly along `hat(e)_(z)`. Obvioulsy the surface current densityin, `vec(J)_(s) = (I)/(h) [sqrt(1 - (4//2 pi R)^(2)) hat(e)_(varphi) + (h)/(2PI R) hat(e)_(z)]`. By comparision with the case of a selenoid and a hollow straightconductor, we SEE that field inside the coll `= mu_(0) (I)/(h)sqrt(1 - (h//2pi R)^(2))` `(CF. B = mu_(0) nI)` outside only the other term CONTRIBUTES, so `B_(varphi) xx 2pi = mu_(0) (I)/(h) xx (h)/(2pi R) xx 2pi R` or, `B_(varphi) = (mu_(0))/(4pi). (2l)/(r)`. |
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