# EM , magnetic field at centre of a carrying circular loop

**I**

**Okay so I’m trying to do this by both Amp’s Law and Biot Savarts Law, and I can’t get my answers to agree. **

First method – Biot Savarts Law:

**B**=[itex]\frac{I\mu_{0}}{4\pi}[/itex][itex]\int[/itex][itex]\frac{dl X \hat{n}}{n^{2}}[/itex]

n[itex]^{2}[/itex]=R[itex]^{2}[/itex]

**dl**[itex]X[/itex][itex]\hat{n}[/itex]=**dl** (*as | n|=R is always perpendicular to a given line element dl)*

=> **B**=[itex]\frac{I\mu_{0}}{4\pi}[/itex][itex]\int[/itex][itex]\frac{dl X \hat{n}}{n^{2}}[/itex]=[itex]\frac{I\mu_{0}}{4R^{2}\pi}[/itex][itex]\int[/itex]dl=[itex]\frac{I\mu_{0}}{4R^{2}\pi}[/itex]2R[itex]\pi[/itex]=[itex]\frac{\mu_{0}I}{2R}[/itex]

Second method – Ampere’s Law:

[itex]\oint[/itex]**B.dl**=[itex]\mu_{0}[/itex]I(enclosed)

So B[itex]\oint[/itex]**dl**=[itex]\mu_{0}[/itex]I

**B**2[itex]\pi[/itex]R=[itex]\mu_{0}[/itex]I

=> **B**=[itex]\frac{\mu_{0}I}{2πR}[/itex]

**Thanks in advance.**

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