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- Homework Statement
- A thin wire that carries the current I is bent in a heart-shaped curve according to the equation r_c=r_0 e^k|phi| for |phi|<= pi, where r_c is the distance from origo to a point on the curve. Calculate the magnetic flow B in origo.

- Relevant Equations
- Biot Savarts Law

Hi,

So I know I am to use Biot Savarts law d

This makes (

From previous questions, I have defined d

Usually its d

My professor tells me to use d

Why is this intuitively correct? I am having some problem wrapping my head around this. How can I derive it from the d

//

So I know I am to use Biot Savarts law d

**B**= (my_0/4pi)* (I d**l**x (**r-r'**)/|**r-r'**|^3 where**r=0**because its in origo and**r'=**r'_c(**r'_hat**).This makes (

**r-r'**)= -r'_c(**r'_hat**) and |**r-r'**|^3= r_c^3.From previous questions, I have defined d

**l'**as the infinitesimal displacement of**r'**(phi) when phi' is increasing with dphi along the curve.Usually its d

**l**'/dphi = r_hat --> d**l**= r_hat dphi and then I use Biot Savarts law. However I get wrong result here.My professor tells me to use d

**l**=r_c' dphi' phi_hat + dr'_c r_hat_c.Why is this intuitively correct? I am having some problem wrapping my head around this. How can I derive it from the d

**l**' expression? Or know if there are any other shapes that do not only depend on phi.//