# Flower-like loop

The figure shows a circular loop of radius $$R$$ (black curve) that has been harmonically deformed into a flower-like curve (blue curve) given by the equation in polar coordinates $r(\theta)= R (1+\varepsilon\cos(n \theta)) \quad \text{with} \quad \varepsilon=0.5 \quad \text{and} \quad n=5.$

A current $$I_{0}$$ flowing in the circular loop produces a magnetic field $$B=1~\text{mT}$$ at the center O. Determine the magnitude of the magnetic field in mT at O when the same current, $$I_{0}$$, flows in the flower-like loop. The following integral may be useful: $\int_{0}^{2\pi}\frac{dx}{1+\varepsilon \cos(x)}=\frac{2\pi}{\sqrt{1-\varepsilon^{2}}}.$

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