Magnetic field generated by current in semicircular loop at a point on axisby SOMEBODYCOOL Tags: biotsavart, magnetic field, magnetic fields, semicircle 

#1
Mar1310, 10:11 PM

P: 5

1. The problem statement, all variables and given/known data
Determine the magnetic field strength and direction at a point 'z' on the axis of the centre of a semicircular current loop of radius R. 2. Relevant equations Biot Savart Formula [tex]d\vec{B}=\frac{\mu_{0}Id\vec{r}\times\hat{e}}{4\pi\vec{R}\vec{r}^{2}}[/tex] e being the unit vector from r to R 3. The attempt at a solution A much simpler problem is a full current loop, because one component of the magnetic field cancels out. For this problem, you'd have to deal with the halfcircle arc and the straight line base separately. I was also wondering whether its easier to calculate the z and x components of B separately as well... One component is straightforward enough... I just really don't understand where to start. 



#2
Mar1410, 12:15 AM

HW Helper
P: 5,004

This should be a pretty straightforward application of the BiotSavart Law. Start by finding expressions for [itex]\textbf{r}[/itex], the position vector for a general point on the semicircular arc, and [itex]\textbf{R}[/itex] the position vector for a general point on the [itex]z[/itex]axis....what do you get for those?...What does that make [itex]\hat{\mathbf{e}}[/itex]? What is [itex]d\textbf{r}[/itex] for a semicircualr arc?
To makethings easier, you will want to use cylindrical coordinates. 



#3
Mar1410, 03:23 PM

P: 5

So, the parametric representation of a point on the semicircle would be (0, bcos(t), bsin(t)) where b is the radius of the semicircle.
The vector R is just [d, 0, 0] where d is the distance on the axis of the point and then the e is the unit vector from Rr But what's dr? And where does the switch to cylindrical coord come in? 



#4
Mar1410, 04:34 PM

P: 5

Magnetic field generated by current in semicircular loop at a point on axis
I think I got it. Thanks



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