Sriman Dutta Posted December 23, 2016 Share Posted December 23, 2016 (edited) Hello everyone, As shown in the diagram, there is a semi-circular loop of current carrying wire, such that point P is the centre of the semi-circle and r is the radius. What shall be the magnetic flux density at the centre P? I presume that the diagram must be treated by the Ampere's Law. So, [math] B=\frac{\mu_0 I}{2\pi r}[/math] Edited December 23, 2016 by Sriman Dutta Link to comment Share on other sites More sharing options...
Bender Posted December 23, 2016 Share Posted December 23, 2016 Half a loop, so half the flux density of a full loop. Link to comment Share on other sites More sharing options...
Sriman Dutta Posted December 23, 2016 Author Share Posted December 23, 2016 So, the denominator should be [math]4\pi r [/math] Link to comment Share on other sites More sharing options...
Bender Posted December 23, 2016 Share Posted December 23, 2016 On my phone, right now, but I think the pi is canceled out. Link to comment Share on other sites More sharing options...
Sriman Dutta Posted December 24, 2016 Author Share Posted December 24, 2016 On my phone, right now, but I think the pi is canceled out. Why and how ? Link to comment Share on other sites More sharing options...
Bender Posted December 24, 2016 Share Posted December 24, 2016 Why and how ? Because you integrate over half a circle, which in this case comes down to a multiplication with [math]\pi R[/math] Derivation for full loop Link to comment Share on other sites More sharing options...
Sriman Dutta Posted December 24, 2016 Author Share Posted December 24, 2016 Thanks Bender......... Here I summarize all the formulae for four different situations. For a straight wire carrying current [math] B=\frac{\mu_0 \mu_r I}{2 \pi r}[/math] For a single loop of wire [math] B=\frac{\mu_0 \mu_r I}{2r}[/math] For a solenoid of length [math]l[/math] and having [math]n[/math] turns [math] B=\frac{\mu_0 \mu_r nI}{l}[/math] For a toroid of single turn and of radius [math]r[/math] [math] B=\frac{\mu_0 \mu_r nI}{2 \pi r}[/math] Are they correct?? Link to comment Share on other sites More sharing options...
Bender Posted December 25, 2016 Share Posted December 25, 2016 Yes. I double checked with the hand book I use (Giancoli ) Link to comment Share on other sites More sharing options...
Sriman Dutta Posted December 26, 2016 Author Share Posted December 26, 2016 Thanks. Link to comment Share on other sites More sharing options...
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