A current ii flows in a long single-layer solenoid with cross-sectional radius rr. The number of turns per unit length of the solenoid equals nn. If the limiting current at which the winding may rupture if the tensile strength of the wire is equal to flimflim is ilim=xflim0nrilim=xflim0nr. Find xx and state whether the value of xxis positive or negative.
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A current I flows in a long single-layer solenoid with cross-sectional radius R. The number of turns per unit length of the solenoid equals n. Find the limiting current at which the winding may rupture if the tensile strength of the wire is equal to F
Explanation:
The magnetic induction B in the solenoid is given by B = μ0 nl. The force on an element dl of the current carrying conductor is,
df=1/2meu not the force on conductar isisdf= 1/2 meu not
This is radially outwards. The factor 1/2 is explained above. To relate dF to the tensile strength Flim we proceed as follows. Consider the equilibrium of the element dl. The longitudinal forces F have a radial component equal to
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